Characteristics of Noise and Photon Statistics of Fiber ...

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Characteristics of Noise and Photon Statistics of

Fiber Components in Electro-Optical Systems

By

Cheng Zhao

Submitted in Partial Fulfillment of the

Requirements for the Degree

Doctor of Philosophy

Supervised by

Professor William R. Donaldson

Program of Materials Science

Department of Mechanical Engineering

Arts, Sciences and Engineering

Edmund A. Hajim School of Engineering and Applied Sciences

University of Rochester

Rochester, New York

2012

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Dedicated to my parents…

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Biographical Sketch

Cheng Zhao was born in Shanghai, China, in 1979. She attended Shanghai Jiao Tong

University, China, from 1998 to 2005, graduating with a Bachelor of Science degree in

2002 in Materials Science and Engineering, and a Master of Science degree in 2005 in

Materials Science. She came to the University of Rochester in the fall of 2005 and began

graduate studies in the program of Materials Science, the department of Mechanical

Engineering. She received the Master of Science degree in 2007 and continued the

pursuit of the Doctor of Philosophy degree. Under the supervision of Professor William R.

Donaldson, she carried out her doctoral research in the characterization of fiber

components in electro-optical systems. She received a Frank Horton Graduate Fellowship

from the Laboratory for Laser Energetics from 2011 to 2012.

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Acknowledgement

First and foremost, I would like to express my sincerest gratitude to my advisor,

Professor William R. Donaldson who has supported me throughout my research with

great patience and knowledge. This thesis would not have been possible without his

enlightened guidance.

I feel very fortunate to work with Prof. Donaldson. With his encouragement and support,

I had the opportunities to audit and watch many courses from the Institute of Optics. I

have learned so much from him in fiber optics and electronic testing methods. It is under

his guidance that I began to study and use Matlab for data acquisition and analysis. He

also helped me build my confidence on theoretical work by teaching me step by step how

to apply finite difference method in simulations.

I would like to thank Prof. Roman Sobolewski. It is the experience working with him that

I began to learn optics and to do experiments with optical components. Honestly, the first

time I saw real lasers, lens, polarizers (at that time, I had no idea what it is) and even

optical tables was in his lab. Most of my knowledge on experimental optics came from

the working experience with him and his group members.

I would also like to thank all my friends in lab, Dr. Shuai Wu, Dr. Xia Lisa Li, Dr. Dong

Pan, Dr. Daozhi Wang, Dr. Allen Cross, Dr. Hiroshi Irie and Dr. Jie Zhang. Without their

help, my research work would have been far more difficult than it was. Special thanks to

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Dr. Yijing Fu from Prof. Fauchet‟s group. I got to learn a lot from his wide knowledge in

optics and programming and his personality.

Finally, I would like to thank my parents for their unconditional love, support and

encouragement in my life.

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Abstract

This thesis presents a comprehensive study of the role of the fiber replicator in electro-

optical systems.

In the all fiber optical diagnostic system for the National Ignition Facility‟s DANTE data

acquisition system running at 1550nm, the 8× fiber replicator was used to increase the

SNR (Signal to Noise Ratio) of single-shot, electrical pulse measurements. In the system,

Mach-Zehnder modulators were used to convert the electrical signals into optical signals.

The fiber replicator was used to create identical copies of the optical signals. A High

SNR was achieved through the averaging of these duplicated signals. Erbium-doped fiber

amplifiers (EDFAs) were built to amplify the optical signals after the fiber replicator.

The EDFAs applied in the DANTEEO system should have high gain, low noise, low

background signals and high pulse-shape fidelity. In this thesis, we discussed the effect of

different configurations and the type of Er-doped fibers on the gain and noise

performance of EDFAs. We also used a simplified model for dynamic gain in EDFAs to

explore the effect of the EDFA on the shape of the amplified pulse. Based on this model,

the calculated pulse-shape distortions were found to be dependent on the EDFA

configuration and the optical gain.

We also investigated the photon statistics with the fiber replicator in a photon

entanglement system. The entangled photons were created through the up-conversion and

down-conversion of a Q-switch laser beam running at 1053nm. The different behavior

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between entangled photon and non-entangled single photons in the system with the fiber

replicator are discussed.

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Contributors and Funding Sources

Unless otherwise specified, the author performed all experimental procedure and

simulations presented in this Ph.D. thesis. Other contributions from colleagues and

collaborates are listed below:

The fiber replicators (both 8× replicator in Chapter 3 and 64× replicator in Chapter 6)

were built by Richard Roides at the Laboratory for Laser Energetics.

The NIF DANTEEO system was assembled by Dr. Limin Ji.

The dither suppression system for MZMs was built by Kirk Miller from National

Security Technologies LLC.

This work was supervised by a dissertation committee consisting of Professors William R.

Donaldson (advisor), Roman Sobolewski, and Qiang Lin of the Department of Electrical

and Computer Engineering and Professor John C. Lambropoulos of the Materials Science

Program and the Department of Mechanical Engineering. Graduate study was supported

by a Frank Horton Fellowship from the Laboratory for Laser Energetics. All other work

conducted for the dissertation was completed by the student independently. The work

was supported by the (U.S.) Department of Energy (DOE) Office of Inertial Confinement

Fusion under Cooperative Agreement No.DE-FC52-08NA28302, the University of

Rochester, and the New York State Energy Research and Development Authority.

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Table of Contents

Biographical Sketch ........................................................................................................... iii

Acknowledgement ............................................................................................................. iv

Abstract .............................................................................................................................. vi

Contributors and Funding Sources................................................................................... viii

Table of Contents ............................................................................................................... ix

List of Tables ................................................................................................................... xiii

List of Figures .................................................................................................................. xiv

List of Symbols ............................................................................................................... xxv

Chapter 1: Introduction ................................................................................................... 1

1.1 Single-shot optical pulse measurement with 256-channel fiber replicator ............... 2

1.2 NIF DANTE system ................................................................................................. 3

1.3 Erbium-doped Fiber Amplifiers (EDFA) in modern telecom industry .................... 5

1.4 EDFAs Applied in the DANTEEO System .............................................................. 7

1.5 Thesis Outline ........................................................................................................... 9

Reference ...................................................................................................................... 11

Chapter 2: General principles on fiber components ..................................................... 14

2.1 Fiber components in electro-optical systems .......................................................... 14

x

2.1.1 Fiber Replicator ............................................................................................... 14

2.1.2 Mach-Zehnder Intensity Modulator (MZM) .................................................... 15

2.1.3 Wavelength division multiplexing (WDM) ..................................................... 18

2.2 Erbium-doped fiber amplifier ................................................................................. 19

2.2.1 Spectra of Er3+

dopant in silica fiber and cross sections .................................. 20

2.2.2 Three-level system ........................................................................................... 22

2.2.3 Steady-state gain .............................................................................................. 24

2.2.4 Amplifier noise ................................................................................................ 27

2.2.5 Transient gain................................................................................................... 30

Reference ...................................................................................................................... 35

Chapter 3: Erbium-doped fiber amplifiers (EDFAs) for NIF DANTE system ............ 38

3.1 EO diagnostic system for NIF DANTE (NIF DANTEEO) .................................... 38

3.1.1 The EO system configuration .......................................................................... 38

3.1.2 System specifications of the components ........................................................ 39

3.2 Characterization of the commercial EDFA............................................................. 46

3.3 Characterization of EDFAs ..................................................................................... 53

3.3.1 EDFAs with L-band Er-doped fiber and multi-stage configuration ................ 53

xi

3.3.2 Performance of EDFAs with L-band and/or C-band Er-doped fibers ............. 68

3.3.3 The addition of a holding channel and its effect on EDFA spectrum .............. 84

Reference ...................................................................................................................... 87

Chapter 4: Numerical simulations of transient gains for EDFAs in the DANTEEO

system……… ................................................................................................................... 89

4.1 Simulation method .................................................................................................. 89

4.2 Simulation parameters ............................................................................................ 94

4.3 Simulation results and discussion ......................................................................... 101

4.3.1 Single-stage forward pumping EDFAs .......................................................... 102

4.3.2 Double-stage EDFAs ..................................................................................... 109

4.3.3 Applications of the simulation results in NIF DANTEEO system ................ 118

Reference .................................................................................................................... 123

Chapter 5: General principles on photon entanglements ............................................ 124

5.1 EPR paradox and Entanglement ........................................................................... 124

5.2 Bell-type inequalities ............................................................................................ 126

5.3 Energy-time entanglement .................................................................................... 129

Reference .................................................................................................................... 131

xii

Chapter 6: Experimental Setup and Discussion for two photon entanglement .......... 134

6.1 Experimental Setup ............................................................................................... 134

6.1.1 Light source ................................................................................................... 134

6.1.2 Time-bin entanglement system ...................................................................... 136

6.2 Characterization of photon distribution without SPDC ........................................ 140

6.3 Characterization of time-bin entangled photon distribution ................................. 144

Reference .................................................................................................................... 153

Chapter 7: Conclusions and Future Work .................................................................. 154

xiii

List of Tables

Table 3.1 Parameters for the DFB laser ............................................................................ 39

Table 3.2 Parameters of the commercial EDFA [1]. ....................................................... 46

Table 3.3 Optical Parameters of the EDFA pumping laser [11]. ...................................... 57

Table 6.1 Combinations of APDs and fiber replicator outputs (C1 and C2) .................. 145

xiv

List of Figures

Figure 1.1 Schematic of the single-shot optical pulse measurement system [6]. .............. 3

Figure 1.2 NIF DANTE system illustration (a) and SCD5000s digitizer (b). The parts in

the orange dashed circle are to be replaced with a new EO system. .................................. 4

Figure 1.3 Commercial EDFA has compact size (70×90×12mm) from MANLIGHT (the

picture comes from http://manlight.com/Mini-EDFA-Gain-block.html ). ......................... 6

Figure 2.1 Schematic of a 64-pulse fiber replicator with delay-line configuration. ......... 15

Figure 2.2 Schematic of the Mach-Zehnder Modulator (MZM). ..................................... 16

Figure 2.3 Schematic of a MZM operating in linear range. (The transmission vs. voltage

curve is plotted using Vπ= 5 V and Ф= - 0.4π.) ................................................................ 17

Figure 2.4 Energy level of Er3+

dopant in silica fiber [22]. .............................................. 21

Figure 2.5 The three-level simplified system of Er3+

in glass. ......................................... 22

Figure 2.6 Simulation of the signal gain vs. pump power (a) and vs. the fiber length (b).

The signal is at 1550.116nm, pumping wavelength is 980nm, Er-doped fiber length is

10m, the input signal is -30dBm (0.001mW). This simulation was done with the software

“GainMaster” from Fibercore Limited with the single stage forward pumping setup. .... 27

Figure 2.7 Schematic of the experimental setup for the phase sensitive amplifier. Black

and blue lines represent optical and electrical connections, respectively. The inset plots

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show the input spectra of phase-insensitive and phase-sensitive amplifications,

respectively. BER sensitivity was measured at port A and B by considering PSA as a pre-

or inline amplifier, respectively. CW, continuous wave; NFA, noise-figure analyzer; OSA,

optical spectrum analyzer; PM, phase modulator; PC, polarization controller; PZT,

piezoelectric transducer; PD, photodetector; TDL, tunable delay line; VOA, variable

optical attenuator; PRBS, pseudo-random bit sequence; BER, bit-error ratio; TX,

transmitter [33].................................................................................................................. 29

Figure 2.8 The typical signal pulse shape in the DANTEEO system. The left corner is a

whole train pulses generated by a fiber replicator. ........................................................... 31

Figure 2.9 An example of the transient response. Inset shows the same transient response

over a long time period. Δt expresses the time span for changing the gain by 0.5 dB from

the initial value after changing the input channel number [37]. ....................................... 34

Figure 3.1 NIF DANTEEO system packed in a black box. .............................................. 38

Figure 3.2 The schematic of the EO system for NIF DANTE (a). The thick black arrows

represent electrical signals and the thin black arrows represent optical signals. Schematics

of 4× (b) and 2× (c) replicator used in the DANTE system shown in (a). ....................... 40

Figure 3.3 Schematic of commercial Mach-Zehnder bias controller [1]. ......................... 43

Figure 3.4 Calibration of both MZ modulators. ................................................................ 43

Figure 3.5 Absorption and emission coefficients in the C-band Erbium-doped fiber [2]. 45

xvi

Figure 3.6 The pulse trains from 4× output with an amplified photodetector (a) and 8×

output amplified by the commercial EDFA with 90 mA pumping current (b). ............... 47

Figure 3.7 The relationship between the amplitude ratio between 4× output signals and

the EDFA pumping current. Curves come from two different measurements. ................ 48

Figure 3.8 The amplified signals with the pumping current at 190 mA. .......................... 49

Figure 3.9 The pulses realigned and normalized based on the first pulse modulated by

Mach-Zehnder #1 (a). The red curve represents the first pulse, the blue curve represents

the last pulse, and the green curve is the averages of each eight replicas. (b) The

calculated SNR vs. time corresponding to the pulses in (a). ............................................ 50




calculated SNR vs. time corresponding to the pulses in (a). ............................................ 51

Figure 3.11 The spectrum of the amplified signals shown in Figure 3.8. The ASE

background is continuous. The duty cycle for the holding channel is about 100%, for two

signals channels (1552nm and 1557nm) is 6.6×10-3

%. .................................................... 52

Figure 3.12 Two-stage dual forward pumping EDFA experimental setup. ..................... 56

Figure 3.13 Two-stage forward and backward pumping EDFA experimental setup. ...... 57

Figure 3.14 The amplified signals with the configuration shown in Figure 3.12. ............ 58

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Figure 3.15 The pulses (from Figure 3.14) realigned and normalized based on the first

pulse modulated by Mach-Zehnder #1 (a). The red curve represents the first pulse, the

blue curve represents the last pulse, and the green curve is the averages of each eight

replicas. (b) The calculated SNR vs. time corresponding to the pulses in (a). ................. 59





Figure 3.17 The amplified signals with the configuration shown in Figure 3.13. ............ 61









Figure 3.20 Comparisons of the SNRs at different signal amplitudes (a) dual forward

pumping scheme, the configuration shown in Figure 3.12 (b) forward and backward

pumping scheme, the configuration shown in Figure 3.13. The dashed blue lines are the

xviii

fittings of the SNR vs. Amplitude. The dashed and point green lines in the two figures are

the SNR at the signal amplitude 0.1 V reading from the oscilloscope. ............................ 64

Figure 3.21 Comparisons of pulse shape with the signals amplified by two EDFAs. ...... 66

Figure 3.22 Two-wavelength pulse trains were generated via AOMs to simulate the

electro-optic measurement system input to the EDFA. .................................................... 68

Figure 3.23 A single-stage EDFA configuration for testing different types of optical fiber.

........................................................................................................................................... 69

Figure 3.24 Signals from a single-stage EDFA with C-band Er-doped fibers. The typical

waveform read directly from the oscilloscope, the pump power is 25mW at 980nm. ..... 70

Figure 3.25 The spectra for EDFAs with C-band Er-doped fibers (a) with different

pumping powers (b) zoom-in the spectra at signal wavelengths from 1545nm-1560nm. 71

Figure 3.26 Signals from single-stage EDFA with the L-band Er-doped fiber. (a) The

typical waveform reading from the oscilloscope, pump power is 100mW. (b) The spectra

under different pump powers. The red circle shows the spectral hole burning (SHB). .... 73

Figure 3.27 The comparison of C- and L- band Er-doped fibers. (a) The whole spectra

range from 1500nm to 1600nm. (b) Spectra around 1540nm to 1560nm. ....................... 75

Figure 3.28 Signals from the single-stage EDFA with C-band + L-band Er-doped fiber. (a)

The typical waveform reading from the oscilloscope, pumping power is 100mW. (b) The

spectra for different pump powers. ................................................................................... 77

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Figure 3.29 Signals from single-stage EDFA with L-band + C-band Er-doped fibers. (a)


spectra with different pumping power. The blue circle illustrates the spectral

characteristic of parasitic oscillations. .............................................................................. 79

Figure 3.30 Free running ASE signals. The left small plot is the corresponding spectral

measurement. .................................................................................................................... 81

Figure 3.31 Comparisons of the EDFA gain spectrum using different Er-doped fibers. . 82

Figure 3.32 The oscilloscope waveform for a double-stage EDFA with C+L configuration.

The two pulse trains (either in black or in red) come from different wavelengths. .......... 84

Figure 3.33 Waveforms of holding and signal channels used in the electro-optic data

acquisition system. ............................................................................................................ 85

Figure 3.34 The gain spectra of the signals as a function of the holding channel power. 86

Figure 4.1 Schematic of the finite difference method in the calculation of the EDFA gain.

........................................................................................................................................... 91

Figure 4.2 The schematic of the finite-difference method applied in the calculation of

transient gain in EDFAs. ................................................................................................... 93

Figure 4.3 Absorption and Emission Coefficients of C- and L-band Erbium-doped fibers

at working wavelengths (a) and pump wavelengths (b). Data comes from [5]. ............... 94

xx

Figure 4.4 The calculated boundary conditions. (a) GainMaster‟s result (b) the

comparison of the simulated result with the GainMaster‟s result (c) the EDFA

configuration for the boundary condition calculated with GainMaster shown in (a). ..... 96

Figure 4.5 The relation between inversion level and different fiber parameters. (a)

Inversion level vs. overlap factor for the pump wavelength (b) Inversion level vs. overlap

factor for signal (ASE) wavelengths (c) Inversion level vs. doping concentration,

assuming overlap factors are 0.5 for both the pump and signal wavelengths. .................. 98

Figure 4.6 The change of optical powers along the fiber length. (a) Pump power, overall

ASE power (from 1450nm to 1650nm) and power loss vs. fiber length (b) ASE power at

different wavelengths vs. fiber length. .............................................................................. 99

Figure 4.7 Waveforms of the signals in the DANTEEO system. ................................... 101

Figure 4.8 Schematic of the single-stage forward pumping EDFA configuration in

simulations. ..................................................................................................................... 102

Figure 4.9 Waveforms and gain plots with 60mW pump power. The signals from the first

and the second channels are shown in (a) and (c). The differences between the

renormalized signals are shown in (b) and (d), corresponding to (a) and (c). ................ 103

Figure 4.10 Simulated results (a) The derivative of the gain with respect to time vs. time

for three channels. (b) The semi-log plots of gain vs. time for two signal channels. ..... 105

Figure 4.11 The amplitude differences under different pump powers. (a) The maximum

values of amplitude difference vs. pumping power (b) The minimum values of amplitude

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difference vs. pumping power. The small plot shows the definition of max and min values

of the amplitude differences............................................................................................ 106

Figure 4.12 Gain and differential gain with different pump powers. (a) 120 mW (b) 180

mW (c) 240 mW (d) 300 mW. ........................................................................................ 108

Figure 4.13 Schematic of the double-stage, forward pumping configuration in simulations.

......................................................................................................................................... 109

Figure 4.14 Waveforms and gain plots with the double stage dual forward pumping

EDFA configuration shown in Figure 4.13. The signals from the first and the second

channels are shown in (a) and (c). The differences between the renormalized signals are

shown in (b) and (d), corresponding to (a) and (c). ........................................................ 110

Figure 4.15 Gain plots for the double stage dual forward pumping EDFA configuration

shown in Figure 4.13. (a) The differential gain for three channels. (b) The semi-log plots

of gain in signal channels. ............................................................................................... 111

Figure 4.16 The change of amplitude differences with different pump powers for the

double-stage forward pumping configuration shown in Figure 4.13. (a) The change of

amplitude differences (max and min) with the change of pump powers for the second

stage, the pumping power for the first stage is 60mW. (b) The change of amplitude

differences (max and min) with the change of pumping powers for the first stage, the

pumping power for the second stage is 60mW. .............................................................. 112

xxii

Figure 4.17 Configuration of a double stage EDFA with forward and backward pumping

scheme............................................................................................................................. 113

Figure 4.18 Waveforms of the forward and backward pumped double-stage EDFA. The

configuration is shown in Figure 4.17. The signals from the first and the second channels

are shown in (a) and (c). The differences between the renormalized signals are shown in

(b) and (d), corresponding to (a) and (c). ........................................................................ 114

Figure 4.19 Gain plots with the forward and backward pumped double-stage EDFA. The

configuration is shown in Figure 4.17. (a) The differential gain for three channels. (b)

Zoom-in of the time region within red dashed line shown in (a). (c) The semi-log plots of

the gain for signal channels............................................................................................. 115

Figure 4.20 The change of amplitude difference with pump power for the double stage

forward and backward pumping scheme. The configuration is shown in Figure 4.17. (a)

The change of amplitude difference (max and min) with the change of pumping power

for the second stage, the pump power for the first stage is 60mW. (b) The change of

amplitude difference (max and min) with the change of pump power for the first stage,

the pump power for the second stage is 60mW. ............................................................. 116

Figure 4.21 Gain vs. Time. (a) the double-stage with dual forward pumping (b) the

double-stage with forward and backward pumping. ....................................................... 117

Figure 4.22 Estimation of the pulse shape distortion resulted from the gain difference

within a single pulse. (a) The calculated differential gain for a double-stage dual-forward

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pumping EDFA, the same Figure as Figure 4.15(a). (b) A typical waveform of a single

pulse in the NIF DANTEEO system. .............................................................................. 119

Figure 4.23 Experimental setup for the simulation of the transient gain for a long time

window. (a) The schematic of the experimental setup. (b) The waveform of the input

signal train of the pulses with two wavelengths. The length of the signal train is about 10

μs. .................................................................................................................................... 121

Figure 4.24 Comparison of the experimental and simulation results. ............................ 122

Figure 5.1 Experimental setup of the HOM model (a) and the interference pattern (b) [26].

......................................................................................................................................... 129

Figure 6.1 Block diagram of the multipurpose Nd:YLF laser (a) the Q-switched pulse (b)

[1]. ................................................................................................................................... 135

Figure 6.2 Schematic of the time-bin photon entanglement system. .............................. 137

Figure 6.3 Calibration of the fiber replicator (a) the oscilloscope waveform (b) the

calculated channel width. ................................................................................................ 140

Figure 6.4 Schematic of the system for characterizing the outputs without SPDC. ....... 141

Figure 6.5 Simultaneous signals from both channels of the fiber replicator. The photons

in this measurement are not entangled. ........................................................................... 142

Figure 6.6 Multiple signals from the APDs. The photons in this measurement are not

entangled. ........................................................................................................................ 143

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Figure 6.7 Amplitude Calibration of the 64× fiber replicator with 12.5 ns channel width.

......................................................................................................................................... 144

Figure 6.8 Signals from the oscilloscope (a) single pulse (b) two pulses in one channel (c)

three pulses in one channel. The photons characterized in this figure are possibly

entangled through SPDC................................................................................................. 146

Figure 6.9 Counts per channel for the fiber replicator (a) and (c) are raw data from output

#1 and #2. (b) and (d) are calibrated data. These counts are for photons under entangled

state. ................................................................................................................................ 147

Figure 6.10 Experimental setup for the determination of pulse locations ...................... 149

Figure 6.11 (a) The difference of time-bin locations for two pulses (b) the distribution of

channel for two pulses. ................................................................................................... 150

Figure 6.12 The events vs. timing difference of two pulses. .......................................... 151

xxv

List of Symbols

SNR signal to noise ratio

EDFA erbium-doped fiber amplifier

EO system electro-optical system

WDM wavelength-division multiplexing

ASE amplified spontaneous emission

SBS stimulated Brillouin scattering

DWDM dense wavelength-division multiplexing

SRS stimulated Raman scattering

V(t) applied electrical signal

Φ(λ) modulator phase bias

Vπ(λ) half-wave voltage of the modulator

d electrode separation

λ optical wavelength

Г(λ) confinement factor

n(λ) index of refraction

r(λ) electrooptic coefficient

Lm electrode length

MZM Mach-Zehnder Modulator

LiNbO3 lithium niobate

CWDM coarse wavelength-division multiplexing

ITU International Telecommunication Union

ESA excited-state absorption

υp signal flux of 1→3 transition

υs signal flux of the 1→2 transition

σp absorption cross section

σs emission cross section

Г32 and Г23 transition possibilities between 3 and 2

xxvi

Г21 and Г12 transition possibilities between 1 and 2

N1, N2 and N3 populations of each level

τ2 lifetime of energy level 2

Ip pumping intensity

Aeff effective area

G signal

NF noise figure

Rd responsivity of an ideal photo detector

SASE spectral density of ASE

nsp spontaneous emission factor

γn and αn emission and absorption constants

DFB laser distributed feedback laser

AOM acoustic optical modulator

sat

pP pumping power for saturated gain

Std (V) standard deviations

SHB spectral hole burning

g0 peak value of gain coefficient

ω frequency of the light

ωa atomic transition frequency

u propagation direction

PZT piezoelectric translator

SHG second harmonic generation

SPDC spontaneous parametric down conversion

BBO barium borate (BaB2O4)

IR infrared

1

Chapter 1: Introduction

The optically assisted diagnostic systems for electrical signals have been investigated for

many years [1]. Many methods have been explored to increase the limit of the dynamic

range and the speed of oscilloscopes. Optical measurements of electrical signals as fast as

15 ps have been achieved through the use of photoconductive Si switches with

transmission line structures [2]. The linear electro-optic effects (Pockels effect) in LiTO3

and GaAs have also been explored in the electro-optical sampling of ultrafast signals [3-

4]. Electrical signals as fast as 1.1 ps have been detected by a two layer GaAs structure

utilizing the intrinsic Franz-Keldysh effect [5]. However, all these diagnostic methods are

based on repetitive signals and do not work in single-shot range.

In recent years, scientists in the Laboratory for Laser Energetics (LLE) have developed

techniques for an optical diagnostic system for the measurement of single-shot electrical

pulses. There are two such systems currently working in LLE. One system is running at

1053nm with a 256× fiber replicator [6]. Another system is the NIF DANTE system used

in the OMEGA facility at the University of Rochester. The working wavelength is

1550nm.

2

1.1 Single-shot optical pulse measurement with 256-channel fiber

replicator

The schematic of the electrical-optical diagnostic system for measuring the pulse shape at

the front end of the OMEGA laser system is shown in Figure 1.1. The CW laser is

running at 1053nm. The optical signal was generated by a fiber Mach-Zehnder electro-

optical modulator fabricated on LiNbO3 [6]. The fiber replicator in this system has a time

window of 12.5 ns. Thus, the pulse width must be less than 12.5 ns to avoid optical

interference between neighboring time windows of the optical replicator. In the system,

there was a two-stage modulator to generate nano-second pulses. Initially, a square

electrical gate pulse was applied to the first modulator to eliminate any light outside of

the temporal duration of the electrical pulse. The second electrical signal drives the

Mach-Zehnder modulator to generate a shaped optical pulse. Because there is a well-

established relationship between the electrical pulse and the optical transmission for the

Mach-Zehnder modulator, it is possible to determine the original input electrical signal of

the Mach-Zehnder modulator by accurately measuring the optical signal out of the Mach-

Zehnder modulator.

Detailed information about how the Mach-Zehnder modulator and the fiber replicator

work will be provided in Chapter 2. The fiber replicator in this system has 256 channels

and 12.5 ns temporal separation, which means the original signal after the amplifier will

have a total of 256 copies with about 12.5 ns pulse separation. As this fiber replicator is a

passive element, the power of each replica would be around 1/256 of the original single

3

pulse in terms of the conservation of energy, without considering any other loss. So,

optical amplifiers are needed to amplify the signals for detection in an oscilloscope and to

achieve a high SNR. An Yb-doped fiber amplifier and a regenerative amplifier were used

as optical pre-amplifiers for the 1053-nm system [7-8]. The train of replicated optical

pulses was measured with a photodiode (Discovery Semiconductor DSC30S) and a

digital sampling oscilloscope (Tektronix TDS6154c). By temporally realigning and

amplitude averaging, optical signals with dynamic range as high as 1800:1 can be

measured. An inverse transfer function is applied to the processed optical pulse to trace

back to the input electrical pulse. Since this system was used to measure optical pulses,

the distortion introduced by the pre-amplifiers was irrelevant.

Figure 1.1 Schematic of the single-shot optical pulse measurement system [6].

1.2 NIF DANTE system

The DANTE system is multi-channel soft x-ray spectrometers at the National Ignition

Facility (NIF) at Lawrence Livermore National Laboratory and the OMEGA facility at

4

the University of Rochester [9]. They are used to measure radiation drive temperatures

produced in the hohlraums.

(a)

(b)

(b)

Figure 1.2 NIF DANTE system illustration (a) and SCD5000s digitizer (b). The parts in

the orange dashed circle are to be replaced with a new EO system.

5

Each DANTE Channel uses two SCD5000 transient digitizers. There are 18 channels per

DANTE and two DANTE instruments on the NIF target chamber for a total of 72

SCD5000s. The SCD5000 transient digitizers have 6 GHz bandwidth, 900:1 dynamic

range and fixed number (1000) of temporal resolution elements. However, these

digitizers are twenty years old and will need to be replaced soon. FTD10000 scopes are

the only direct replacement option, but an FTD10000 costs about $120K per channel.

Considering each DANTE system requires 36 scopes and 2 spares, this will cost a total of

$5 million. Besides, FTD10000 scopes have a life span of 5000 hours while the current

DANTE system will reach 5000 hours in about 2 years. So the new EO system was

designed as a replacement for SCD5000 with higher bandwidth, low noise, lower

maintenance, longer life time, and lower cost. This all-fiber EO system includes the

electro-optical modulators which convert the electrical signal into a modulated optical

signal and makes use of fiber replicators for high SNR, high pulse-shape fidelity optical

diagnostics. A major portion of this thesis is devoted to the improvement of the 1550nm

version of the EO diagnostic system. This is the system that has the most general use.

1.3 Erbium-doped Fiber Amplifiers (EDFA) in modern telecom

industry

The working wavelength of Erbium-doped fibers ranges from 1520nm to 1620nm which

covers most of both the C (conventional band, 1535nm-1565nm) and the L (long band,

6

1565nm-1625nm) telecommunication wavelength ranges [10]. Since the late 1980‟s,

Erbium-doped fibers have been developed to amplify signals in the telecomm bands [11].

Besides their wide amplification band, Erbium-doped fiber amplifiers (EDFAs) have

many other advantages. They are compact-sized, in-line amplifiers, as shown in Fig 1.3.

As they do not need complicated alignment techniques and therefore avoid high

maintenance costs. EDFAs can be configured to have high gain and low noise. For these

reasons, EDFAs are widely used in the modern telecomm industry, especially working

together with the wavelength-division multiplexing (WDM) for multi-wavelength and/or

multi-channel digital signals.

Figure 1.3 Commercial EDFA has compact size (70×90×12mm) from MANLIGHT (the

picture comes from http://manlight.com/Mini-EDFA-Gain-block.html ).

Many efforts have been made to improve the performance of EDFAs such as gain-

flattening and gain clamping. Investigations of gain-flattened EDFAs over a wide spectral

range have demonstrated a gain flatness of less than 0.7dB over more than 35nm band

http://manlight.com/Mini-EDFA-Gain-block.html

7

width by using acousto-optic filters [12]. Other efficient techniques for gain flattening

include high-birefringence fiber loop mirror, different compositions and dual-core

Erbium-doped fiber, equalizing film, fiber Bragg gratings and mechanically induced

microbending fiber gratings [13-19]. EDFAs with WDMs applied in modern optical

network systems have to deal with gain variation problems resulting from adding and

dropping channels or the sudden failure of components. Gain-clamping techniques have

been used to prevent performance degradation, severe service impairment or the

appearance of optical nonlinearities which resulted from a sudden change of gain [20-22].

A variety of solutions have been employed to stabilize the gain, which are mostly based

on using a part of signal, pumping or amplified spontaneous emission (ASE) as the

feedback either via a cavity loop or fiber gratings [23-28]. Stimulated Brillouin

scattering (SBS) also can be used in the feedback to monitor signal gains [29].

After more than twenty years of continuous efforts on improvement, EDFA technologies

have become quite sophisticated.

1.4 EDFAs Applied in the DANTEEO System

Although there are sophisticated commercial EDFAs available, there is still a need to

develop an EDFA for this particular application because the DANTEEO system has

special requirements that are different from standard telecom applications.

8

The signals in the DANTEEO system are analog signals, while the signals are

normally digital signals in standard telecom. So the EDFA in the DANTEEO

system should have high signal to noise ratio (estimated to be 200:1) and high

pulse-shape fidelity.

The EDFA in the DANTEEO system is designed to amplify signals at multi-

wavelengths. The DANTEEO system is designed for up to eight wavelengths

(corresponding to ITU-200 and/or DWDM channels) in each channel. So the

EDFA should amplify signals with up to eight different wavelengths. As the

DWDM channels range from 1547.72nm to 1558.98nm, it is quite easy to get

uniform gain for all wavelengths. But the narrow spectral separation will also

cause crosstalk, which will affect signal pulse shape diagnostics. Unlike standard

telecom system, only one wavelength will be in the system at any particular time.

The temporal separation of the wavelengths will affect the gain dynamics of the

EDFA.

For each wavelength, the signal has a train of pulses with temporal separation.

The signal amplitude changes fast (~ns) compared with the transit time in

Erbium-doped fibers. So the EDFA is not working under steady state or quasi

steady-state.

The final signal pulse shape diagnostics will be based on the mathematical

average of those pulses in the time domain. So the gain dynamics, if different for

individual pulses, will also affect the final signal pulse shape.

9

The signal pulse train was generated by a fiber replicator. The individual pulses

will have different polarizations as they go through different optical paths within

the fibers. So the polarization related optical fiber components such as the

Faraday isolators are not suitable in this EDFA configuration as they don‟t affect

all pulses evenly.

1.5 Thesis Outline

This thesis consists of two parts, corresponding to the two optical pulse diagnostic

systems currently working in LLE. The major part, Part I, is noise characterization in Er-

doped fiber amplifier (EDFA) used in the single-shot electro-optical diagnostic system

NIF DANTEEO. The target of this experiment is to design an Er-doped fiber amplifier to

replace the commercial EDFA in the current system setup. Low noise, low background

signal, larger amplification and good pulse shape restoration are the major considerations.

The first part of Chapter 2 will introduce the basics of some fiber elements used in the

DANTEEO system. The second part of Chapter 2 covers the fundamental mechanisms of

the gain process, including three-level amplification basics, absorption and emission

cross sections, and amplified spontaneous emission. The experimental setup and the

discussion of the results will be in Chapter 3. The discussion will emphasize on how the

Er-doped fiber length and pump powers affect both the noise and the shape restoration.

The numerical simulation of the EDFA gain dynamics will be in Chapter 4. We will

discuss how the difference in gain dynamics affects pulse shapes.

10

Part II is the photon statistics with the fiber replicator in a photon entanglement

system. Originally this section started as an investigation of the noise in fiber

replicators as the signal approached the single photon level. This investigation

expanded into an investigation of the photon entanglement. Chapter 5 will emphasize

the basic idea and the progress of our photon entanglement investigation. The detailed

experimental setup (including the complete up-conversion and down-conversion, and

the alignment process) and the results will be presented in Chapter 6. The different

behavior between an entangled photon and a non-entangled photon in the system with

the fiber replicator will be discussed.

Chapter 7 is dedicated to the conclusions of this thesis and a description of the future

work.

11

Reference

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Analog-to-Digital Converter With Time Stretch Preprocessor”, IEEE Photon. Technol.

Lett., vol. 14, No. 5, 2002.

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3. J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electrooptic sampling

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4. G. A. Mourou and K. E. Meyer, “Subpicosecond electro‐optic sampling using coplanar

strip strip transmission lines”, Appl. Phys. Lett. vol.45, pp. 492, 1984.

5. J. F. Lampin, L. Desplanque, F. Mollot, “Detection of picosecond electrical pulses

using the intrinsic Franz–Keldysh effect”, Appl. Phys. Lett., vol. 78, pp. 4103, 2001.

6. W. R. Donaldson, J. R. Marciante, R. G. Roides “An Optical Replicator for Single-

Shot Measurements at 10 GHz With a Dynamic Range of 1800:1”, IEEE Journal of

Quantum Electronics, vol. 46, No.2, 2010.

7. J. R. Marciante, J. D. Zuegel, “High-gain, polarization-preserving, Yb-doped fiber

amplifier for low-duty-cycle pulse amplification”, Appl. Opt., vol. 45, pp. 6798, 2006.

8. A. V. Okishev and J. D. Zuegel, “Highly stable, all-solid-state ND:YLF regenerative

amplifier”, Appl. Opt., vol. 43, pp. 6180, 2004.

9. Donald Pellinen, Matthew Griffin, National Security Technologies, LLC (NSTec).

Livermore Operations (LO), DOE/NV/25946-086.

10. Ramaswami, Rajiv “Optical Fiber Communication: From Transmission to

Networking”, IEEE Communications Magazine, 50th Anniversary Commemorative Issue,

May 2002.

11. R.J. Mears, L. Reekie, I.M. Jauncey, D. N. Payne: “Low-noise Erbium-doped fiber

amplifier at 1.54μm”, Electron. Lett, vol. 23, No. 19, Sep 1987.

12. Hyo Sang Kim, Seok Hyun Yun, Hyang Kyun Kim, Namkyoo Park, and Byoung

Yoon Kim, “Actively Gain-Flattened Erbium-Doped Fiber Amplifier Over 35 nm by

Using All-Fiber Acoustooptic Tunable Filters”, IEEE Photon. Technol. Lett., vol. 10, No.

6, June 1998.

13. Shenping Li, K. S. Chiang, and W. A. Gambling, “Gain Flattening of an Erbium-

Doped Fiber Amplifier Using a High-Birefringence Fiber Loop Mirror”, IEEE Photon.

Technol. Lett., vol. 13, No. 9, Sep 2001.

http://ieeexplore.ieee.org/iel5/35/21724/01006983.pdf



12

14. S. Yoshida, S. Kuwano and K. Iwashita, “Gain-flattened EDFA with high Al

concentration for multistage repeatered WDM transmission systems”, Electron. Lett, vol.

31, No. 20, Sep 1995.

15. Hirotaka Ono, Makoto Yamada, Terutoshi Kanamori, Shoichi Sudo, and Yasutake

Ohishi, “1.58μm Band Gain-Flattened Erbium-Doped Fiber Amplifiers for WDM

Transmission Systems” , Journal of Lightwave Technology, Vol. 17, No. 3, 1999.

16. H. J. Chen and X. L. Yang, “Gain Flattened Erbium-doped Fiber amplifier Using

Simple Equalizing film”, International Jounal of Infrared and Millimeter Wves, vol. 20,

No. 12, 1999.

17. Yi Bin Lu and P. L. Chu, “Gain Flattening by Using Dual-Core Fiber in Erbium-

Doped Fiber Amplifier”, IEEE Photon. Technol. Lett., vol. 12, No. 12, Dec 2000.

18. Jeng-Cherng Dung, Sien Chi and Senfar Wen, “Gain flattening of erbium-doped fibre

amplifier using fibre Bragg gratings”, Electron. Lett, vol. 34, No. 6, Mar 1998.

19. IK-BU Sohn, Jang-Gi Baek, Nam-Kwon Lee, Hyung-Woo Kwon and Jae-Won Song,

“Gain Flattened and Improved EDFA Using Microbending Long-period Fiber Grating”,

Electron. Lett, vol. 38, No. 22, Oct 1998.

20. A. K. Srivastava, Y. Sun, J. L. Zyskind, and J. W. Sulhoff, “EDFA transient response

to channel loss in WDM transmission system,” IEEE Photon. Technol. Lett., vol. 9, No. 3,

Mar 1997.

21. Benjamin J. Puttnam, Benn C. Thomsen, Alicia Lopez, and Polina Bayvel,

“Experimental investigation of optically gain-clamped EDFAs in dynamic opticalburst-

switched networks”, Journal of Optical Networking, vol. 7, No.2, Feb 2008.

22. G. Luo, J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, C. Wolf, and M. A.

Ali, “Performance Degradation of All-Optical Gain-Clamped EDFA‟s Due to Relaxation-

Oscillations and Spectral-Hole Burning in Amplified WDM Networks”, IEEE Photon.

Technol. Lett., vol. 9, No.10, Oct1997.

23. Joon Tae Ahn and Kyong Hon Kim, “All-Optical Gain-Clamped Erbium-Doped

Fiber Amplifier With Improved Noise Figure and Freedom From Relaxation Oscillation”,

IEEE Photon. Technol. Lett., vol. 16, No.1, Jan 2004.

24. Y. Zhao, J. Bryce, and R. Minasian, “Gain Clamped Erbium-Doped Fiber Amplifiers-

Modeling and Experiment”, IEEE Journal of Selected Topics in Quantum electronics, vol.

3, No. 4, Aug 1997.

25. T. Subramaniam, M. A. Mahdi, P. Poopalan, S. W. Harun, and H. Ahmad, “All-

Optical Gain-Clamped Erbium-Doped Fiber-Ring Lasing Amplifier with Laser Filtering

Technique”, IEEE Photon. Technol. Lett., vol. 13, No.8, Aug 2001.

13

26. M. A. Mahdi , F. R. Mahamd Adikan, P. Poopalan, S. Selvakennedy, W. Y. Chan, H.

Ahmad, “Gain-clamped fibre amplifier using an ASE end reflector”, Optics

Communications, No. 177, Apr 2000.

27. J. Bryce, G. Yoffe, Y. Zhao and R. Minasian, “Tunable, Gain-clamped EDFA

Incorporating chirped Fibre Bragg Grating”, Electron. Lett, vol. 34, No. 17, Aug 1998.

28. S. W. Harun, S. K. Low, P. Poopalan, and H. Ahmad, “Gain Clamping in L-Band

Erbium-Doped Fiber Amplifier Using a Fiber Bragg Grating”, IEEE Photon. Technol.

Lett., vol. 14, No.3, Mar 2002.

29. Seung Hee Lee and Seong Ha Kim, “All Optical Gain-Clamping in Erbium-Doped

Fiber Amplifier Using Stimulated Brillouin Scattering”, IEEE Photon. Technol. Lett., vol.

10, No.9, Sep 1998.

14

Chapter 2: General principles on fiber components

2.1 Fiber components in electro-optical systems

2.1.1 Fiber Replicator

To characterize single-shot events, an optical pulse can be replicated and averaged with

itself for better signal to noise ratio. Either a fiber resonator or a delay-line (retarding

pulse replicator) enables single-shot self-replication [1-2]. Due to the simple design, ease

of fabrication and constant signal amplitude, the delay-line is the preferred configuration.

The delay-line configuration is composed of a series of 2×2 fused-fiber splitters spliced

with differential delay fibers as illustrated in Fig 2.1. The length of the fiber in the Nth

stage depends on window time and the number of previous stages. In Fig 2.1, the unit

delay time is 12.5 ns (corresponding to 2.5 meters fiber), which means there will be a

total of 2N pulses replicated from the original signal pulse, and the time window for each

pulse is 12.5 ns. The unit delay time also specifies the maximum temporal pulse-width

for the signals. If the signal pulse-width is larger than the unit delay time, there will be

interference between neighboring pulses.

Ideally, the optical power of the original signal will be distributed evenly and all these

duplicates have the same amplitude. However, due to the fiber loss and the deviation

from a perfect 50/50 splitting ratio of the fiber couplers, there will be difference in the

amplitude of each pulse. Therefore, the amplitudes of these duplicated pulses will be

normalized or resized in the post-processing.

15

Figure 2.1 Schematic of a 64-pulse fiber replicator with delay-line configuration.

2.1.2 Mach-Zehnder Intensity Modulator (MZM)

Mach-Zehnder intensity modulator is based on an optical phase modulator and an optical

interferometer in two-arm configuration. Fig 2.2 is the simple illustration of the Mach-

Zehnder modulator. The light input is split into two beams after coupling into the

waveguide, while the output is the interferometric sum of the two beams. Depending on

the phase or optical path difference of two beams, there is a constructive (if the two

beams encounter identical, or even multiples of π in optical path length) or destructive

interference (if the phase difference of two beams are of odd multiples of π) at the output.

This phase or optical path difference is produced by changing the refractive index of the

beam path with an electrical signal. The important feature of the Mach-Zehnder

modulator is that small changes of electrical signal can produce large changes in the

output optical signal, which allows this kind of modulator to be used in a variety of

applications. However, the Mach-Zehnder modulator is very sensitive to slight

environmental changes such as temperature and stress. So in real applications, the Mach-

Zehnder modulator always works with a feedback loop to stabilize the output.

16

In Mach-Zehnder, the electrical signal can be used to change the optical transmission of

the input beam, which can be expressed as [3]:

211 cos sin

2 2 2

V t V tT

V V

(2.1)

V(t) is the applied electrical signal. Φ(λ) is the modulator phase bias. The phase is related

to internal path length mismatch between the two arms and the externally applied bias

voltage. Vπ(λ) is half-wave voltage of the modulator as shown in Figure 2.3. It is defined

as:

32 m

dV

n r L

(2.1)

d is electrode separation, λ is the optical wavelength, Г(λ) is the confinement factor, n(λ)

is the index of refraction, r(λ) is the electrooptic coefficient, Lm is the electrode length.

Figure 2.2 Schematic of the Mach-Zehnder Modulator (MZM).

As described in Equation (2.1), the optical transmission of the MZM will be a sinusoidal

curve with the input electrical voltage. In the analog applications, the complicated non-

LiNbO3

Input Beam Output Beam

DC Bias RF Signals

17

linear transfer function of the MZM is a disadvantage when the amplitude of the

electrical signal is comparable to Vπ [4]. To avoid this condition, the MZM is normally

operated in the linear range.

Figure 2.3 Schematic of a MZM operating in linear range. (The transmission vs. voltage

curve is plotted using Vπ= 5 V and Ф= - 0.4π.)

To operate in linear range, the DC bias of the MZM can be set to any quadrature point

with 50% transmission such as Vπ/2 which is shown as the pink spot in Figure 2.3. Around

Vπ/2 area, the optical transmission is almost linear with the voltage. When a small time

varying signal, V(t), is applied to the MZM (shown as the blue arrows in the figure), the

V

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Voltage (V)

Tra

nsm

issio

n

Vπ

Vπ/2

V(t)

T

18

optical transmission will change linearly with the RF voltage signal (shown as dark red

curve).

The uniaxial crystal lithium niobate (LiNbO3) is commonly used as the waveguide

material in the Mach-Zehnder modulators [5]. LiNbO3 based Mach-Zehnder modulators

have high switching speed (about 20 GHz) which makes them popular in modern

communication systems [6]. Recently, Silicon and polymers are also investigated as

waveguide materials for as fast as 40 GHz switching speed [7-8].

2.1.3 Wavelength division multiplexing (WDM)

In fiber-optical systems, wavelength-division multiplexing (WDM) is a technology which

multiplexes a number of optical carrier signals at different wavelengths onto a single

optical fiber. The WDM components multiply the capacity of the fiber-optical system by

the number of different wavelength channels.

Wavelength multiplexing components are divided into groups such as WDM, CDWDM

and DWDM based on wavelength spacing. WDMs or broad WDMs components

normally work on only two wavelength bands such as 980nm/1550nm and

1310nm/1550nm. The wavelength spacing of the conventional/coarse (CWDM)

wavelength-division multiplexing is 20nm. The International Telecommunication Union

(ITU) specifies eighteen CWDM wavelengths from 1271nm to 1611nm [9]. Dense

WDMs (DWDM) have much narrower wavelength spacing [10]. Practically employed

19

DWDMs are normally spaced at 100GHz (approximately 0.8nm separation in wavelength)

[11]. DWDMs commonly work in the C-band wavelengths, which coincides with the

gain spectrum of EDFAs. So EDFAs have been widely used with DWDM systems to

compensate optical signal transmission loss in modern telecom networks.

To separate wavelengths, optical filters are used in WDMs to remove unwanted channels

or wavelengths such as residual pump powers and broad ASE background after EDFAs.

2.2 Erbium-doped fiber amplifier

An Erbium-doped fiber amplifier (EDFA) is a type of optical amplifier that uses Er-

doped fiber as gain medium to amplify optical signals. The amplification process is, in

essence, the process of stimulated emission of photons from dopant Er3+

ions in the Er-

doped fiber. The EDFA was first demonstrated by a group from the University of

Southampton and another group from AT&T Bell Laboratories at the same year [12-13].

An EDFA can work in a wide bandwidth (20-70nm) within the 1500-1600 nm

telecommunication bands. And it has the advantages of high gain (20-40 dB) and high

output power (>200 mW). Its amplification performance is insensitive to bit rate, input

power, pulse shape, and input wavelength. Because of these features, EDFAs have now

been widely used in modern telecommunications, especially those incorporating WDMs.

20

2.2.1 Spectra of Er3+

dopant in silica fiber and cross sections

The electronic configuration of Erbium is 1s22s

22p

63s

23p

64s

23d

104p

65s

24d

105p

64f

126s

2.

The outer 5s and 5p shells effectively shield inner 4f electrons from significant

interaction with the local crystalline field associated with the charges on neighboring ions

in solid state configurations [14]. In a condensed form, the trivalent Er3+

is the most

stable state. In the ionic Er3+

state, two outer 6s electrons and one inner 4f electron are

removed, and then outer shell electronic configuration becomes 4f11

. 4I15/2 is the ground

state of Er3+

. The radiative transition 4I13/2→

4I15/2 of Er

3+ ion in silica fiber will emit

photons with wavelengths around 1.53 µm [15]. As there are many sublevels in both 4I13/2

and 4I15/2 as shown in Figure 2.4, the emitted photon wavelengths will range from about

1520nm to 1620nm. And this is the working principle of Er-doped fibers as gain media

for light amplifications. Typically the amplification process will include the initial

pumping of Er3+

ions from the ground state 4I15/2 to any higher energy level such as

4H11/2

[16-17]. The relaxation processes between 4H11/2 to

4I13/2 energy levels are predominantly

nonradiative decay. After fast and nonradiative relaxation or decay processes, the ions

will finally drop to metastable 4I13/2 state and be followed by a radiative emission by

4I13/2y→

4I15/2 transition, with a life time about 10 ms. This process is analogous to three-

level systems, especially when pumping at 980nm, 800nm and above [17]. However, we

will still treat 980nm pumped Er-doped fiber as two-level system in the simulations in

Chapter 4 for simplification. As the excited carriers in 4I11/2 are quickly depleted via

nonradiative transition 4I11/2 →

4I13/2, the two-level system is still a good approximation

[18].

21

Figure 2.4 Energy level of Er3+

dopant in silica fiber [22].

For stimulated light amplification in gain media, the stimulated transition cross sections

are very important parameters. The stimulated transition cross sections include absorption

and emission cross sections. In this thesis, we will neglect excited-state absorption (ESA)

in our simulations (although the ESA phenomenon may occur in our system which we

will discuss in Chapter 3). ESA is the process where the upper level populations not only

amplify the input light via stimulated emission but also absorb the pump power and jump

to higher energy levels [19]. This process will decrease the pumping efficiency. ESA can

be neglected for 980nm pumping if the pump powers are not very high [18-21].

Absorption and emission cross sections are hypothetical areas (with the unit m-2

) used to

describe the possibilities of light being absorbed or emitted. These cross sections are

22

different from geometrical cross sections in that they depend on the wavelength of the

incident light and the permittivity [23].

2.2.2 Three-level system

As mentioned in the last section, the amplification process in Er-doped fiber amplifier is

analogous to a three-level system. And therefore, we will simplify the amplification

process in EDFA into a three-level model and then further simplify the model into a two-

level system in the simulations in Chapter 4.

Figure 2.5 The three-level simplified system of Er3+

in glass.

The three-level system model is plotted in Figure 2.5. Energy level “1” is the ground state,

corresponding to energy level 4I15/2 in Er-doped fibers. Energy level “2” is the metastable

level, corresponding to energy level 4I13/2 in Er-doped fibers. Energy level “3” is the

energy level of excited photons, corresponding to 4I11/2 if pumping with 980nm light. The

( 4I11/2 )

1 ( 4I15/2 )

2 ( 4I13/2 )

3

υpσp

υsσs

Γ32

Γ21

23

populations of each level are N1, N2 and N3. The incident light intensity flux at the

frequency corresponding to 1→3 transition is denoted as υp. This transition is the actual a

pumping or light absorption process used in the experiments described in Chapter 3. υs is

the signal flux of the 1→2 transition, corresponding to light emission process. σp and σs

are the corresponding transition cross sections. Г32 and Г23 are the transition possibilities

between level 3 and level 2, Г32 = Г23. In Er-doped fibers, this transition is a non-radiative

system with very fast decay time. Г21 and Г12 are the transition possibilities from level 2

to level 1, and similarly Г21 = Г12. In Er-doped fibers, it is actually the radiative transition

4I13/2→

4I15/2. The rate equations for the population changes are written as [24]:

121 2 1 3 2 1

221 2 32 3 2 1

332 3 1 3

p p s s

s s

p p

dNN N N N N

dt

dNN N N N

dt

dNN N N

dt

(2.2)

Under steady-state, there are no time-dependent variations of populations:

1 2 3 0

dN dN dN

dt dt dt (2.3)

And the total population N is given by:

1 2 3N N N N (2.4)

Based on Equation 2.3, 2.4 and 2.5, the population difference between 4I13/2 and

4I15/2 in

steady state is:

24

212 1

21 2

p p

p p s s

N N

N

(2.5)

The population inversion occurs when N2 ≥ N1. So the threshold for lasing or

amplification is:

21

2

1th

p p

(2.6)

where τ2 is the lifetime of energy level 2, and τ2 = 1 / Г21. The pumping intensity is

defined as Ip = hυp υp. The power is defined as the product of intensity and effective area

P = Ip Aeff. So the threshold pumping power can be expressed as:

21

21

p eff p eff

th

p p

h A h AP

(2.7)

For a pumping wavelength of 980nm, with an absorption cross section σp = 2×10-21

cm2,

lifetime τ2 = 10 ms, effective area Aeff = 20 µm2 (5 μm diameter for core area) for single-

mode fibers, the threshold power is about 2 mW. This demonstrates one important

advantage for EDFAs, i.e. the low threshold pumping power for gain [18].

2.2.3 Steady-state gain

As defined in the last section, the pump (transition 1→3) and the signal (transition 2→1)

photon flux are:

25

s

s

s

p

p

p

I

h

I

h

(2.8)

Assume the light propagation along with z direction, which is actually the optical axis of

the Erbium fiber, and without considering the transverse field along the fiber, which

simplifies this propagation process into a one-dimensional problem.

After a length of Δz of Er-doped fiber, the change of photon flux in both pump and signal

are:

2 1

3 1

ss s

p

p p

dN N

dz

dN N

dz

(2.9)

Combined with Equation 2.9 and Equation 2.6, the change of photon flux along the fiber

can be described as:

21

21

2

p p

pss s

p p s s

p s

I

hdII N

I Idz

h h

(2.10)

In terms of the above equation, we can find that the role of Er-doped fibers in optical

systems depends on the pump power and the cross section for the pumping wavelength. If

the numerator in the above equation is less than zero, for example a small pump power,

the Er-doped fiber is actually working as an attenuator in the system. The numerator

26

must be larger than zero for real amplification, which results in the threshold condition

for pumping power Ith = hυp/σpτ2. For pump powers, we have the similar equation:

21

21

2

s s

p sp p

p p s s

p s

I

dI hI N

I Idz

h h

(2.11)

For convenience, the pump and the signal flux are normalized by pump threshold. The

new and normalized pump and signal flux are:

/

/

p p th

s s th

I I I

I I I

(2.12)

If the signal is far away from saturation, the signal propagation can be expressed in a

simple format:

0 exp

1

1

s s p

p

p s

p

I z I z

IN

I

(2.13)

αp is defined as gain coefficient. The signal gain (G) with specific length of Er-doped

fiber is defined as:

1010log0

s

s

I z LG

I z

(2.14)

Figure 2.6 is the example of simulations of gain along the fiber length with the

commercial software “GainMaster” (the free commercial software comes from Fibercore

27

Limited, for Erbium Doped Fiber Amplifier Simulation). The plots show the relation of

gain and pumping power for a 10m Er-doped fiber with 980nm pumping wavelength.

Although the commercial software can be used to calculate most of the parameters such

as gain, ASE and noise configuration, all those calculations are based on steady-state

conditions (Equation 2.4). If the signals are not CW or quasi-CW, the EDFA is not

operating under steady-state. Under these conditions, we cannot directly use the results

from the commercial software.

0 5 10 15 20 25 30 35 40 45 50

-40

-30

-20

-10

0

10

20

30

40

Pumping power (mW)

Ga

in (

dB

)

0 1 2 3 4 5 6 7 8 9 10

-5

0

5

10

15

20

25

30

35

Length (m)

Gain

(dB

)

(a) (b)

Figure 2.6 Simulation of the signal gain vs. pump power (a) and vs. the fiber length (b).

The signal is at 1550.116nm, pumping wavelength is 980nm, Er-doped fiber length is

10m, the input signal is -30dBm (0.001mW). This simulation was done with the software

“GainMaster” from Fibercore Limited with the single stage forward pumping setup.

2.2.4 Amplifier noise

Inevitably, all amplifiers degrade the signal-to-noise ratio (SNR) of the system because of

the extra random (no fixed polarization, phase, frequency and direction) amplified

28

spontaneous emission (ASE). The extent of the degradation is quantified by the

parameter NF, noise figure. It is defined as [15-16]:

1010log in

out

SNRNF

SNR (2.15)

(SNR)in and (SNR)out are the input and output power signal-to-noise ratios, respectively.

For an amplifier with the gain G, the SNR of the input signal is given by [25]:

2

in

in

PSNR

h f

(2.16)

The (SNR)out can be expressed as:

2

2 4 2

d in in

outASE

R GP GPSNR

S h f

(2.17)

σ2 is the variance of photocurrent, Rd is the responsivity of an ideal photo detector with

unit quantum efficiency, SASE is the spectral density of ASE given by:

0 1ASE spS n h G (2.18)

nsp is the spontaneous emission factor, or the population-inversion factor defined as:

2

2 1

ssp

s p

Nn

N N

(2.19)

Substituting Equation 2.17-2.20 into Equation 2.16, the noise figure can be expressed as

[14-15]:

29

10 10

2 1 110log 10log 2 3

sp

sp

n GNF n dB

G G

(2.20)

The approximation in the above equation is valid when gain G >> 1. Under ideal

conditions, all population at ground level (level 1) is inverted which makes N1 = 0 and

then nsp = 1. And therefore, 3 dB is the theoretical limit for noise figure in phase-

insensitive amplifiers.

Figure 2.7 Schematic of the experimental setup for the phase sensitive amplifier. Black

and blue lines represent optical and electrical connections, respectively. The inset plots

show the input spectra of phase-insensitive and phase-sensitive amplifications,

respectively. BER sensitivity was measured at port A and B by considering PSA as a pre-

or inline amplifier, respectively. CW, continuous wave; NFA, noise-figure analyzer; OSA,

optical spectrum analyzer; PM, phase modulator; PC, polarization controller; PZT,

piezoelectric transducer; PD, photodetector; TDL, tunable delay line; VOA, variable

optical attenuator; PRBS, pseudo-random bit sequence; BER, bit-error ratio; TX,

transmitter [33].

30

Recently research on fiber amplifiers shows that phase sensitive amplifiers have a better

NF, a theoretical 0 dB noise figure (NF) [26]. Low NF has been achieved in both high

frequency (16GHz) and low frequency region [27-32]. The lowest NF that has been

achieved is 1.1 dB (the experimental setup is shown in Figure 2.7) [33]. Despite the

advantage of high NF, phase sensitive amplifiers are far more complicated systems than

phase insensitive amplifiers such as EDFAs, which limit their commercial applications.

2.2.5 Transient gain

The EDFA gain derived in Chapter 2.2.3 is based on the steady-state assumption. For the

steady-state assumption to be valid, the change of signal power should be slow compared

to the optical transit time of the gain media (Er-doped fibers).

However, this assumption will not be valid if there are sudden changes in the number of

channels or if the signal powers change rapidly. The first situation is quite normal in

modern optical network systems for signal channels add-on or drop-off or the sudden

failure of some components. The second situation happens in the DANTEEO system. The

typical signal waveform in the DANTEEO system is shown in Fig 2.8. Assuming the

length of the Er-doped fiber is 10 m with the refractive index 1.5. So the optical transit

time is 50 ns, while the signals in the DANTEEO system change amplitude within ~ns.

For such fast signal power changes, the EDFA is not working under steady-state range

but in transient range.

31

50 60 70 80 90 100 110 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (ns)

Norm

aliz

ed A

mplit

ude

Figure 2.8 The typical signal pulse shape in the DANTEEO system. The left corner is a

whole train pulses generated by a fiber replicator.

A model for transient gain in EDFA has been derived and can deal with the gain

dynamics in the DANTEEO system based on the following assumptions [21, 34-35]:

The EDFA model is based on a two-level system. Although our system will be

more accurately simulated by a three-level model, a two-level system is still a

good approximation as the lift time of 4I11 is very short compared with our signal

time width and the life time of 4I13 .

We will neglect excited-state absorption. This has been stated in Chapter 2.2.1.

The gain spectrum is homogenously broadened and the time scale for such

broadening is much faster than any relevant optical process.

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (ns)

Norm

aliz

ed A

mplit

ude

32

Gain saturation by ASE is negligible compared to the saturation by the signals.

This assumption is valid for the gain below 20dB. In our system, the gain is

normally below 20dB. Or the gain spectrum is adjusted by a holding channel so

that the gain will not be saturated by ASE even under higher gain. We will discuss

gain-flattening and the use of a holding channel in Chapter 3.

Signal power changes slowly compared to the transit time of light going through

the Er-doped fiber. In the DANTEEO system, the signals do not satisfy this

requirement. However, we use the finite difference method and divide the whole

fiber length into very small steps. During each small step (the step is 25ps or 50ps

in time), the signals (power changes in ~ns level) can be regarded as quasi-CW

sources.

The area of the Er-doped active region is small compared to the optical mode at

the signal wavelength. This assumption allows the overlap factor for signal

wavelength to be kept constant and independent of optical power.

The pumping wavelength is treated the same as the signal wavelengths only with

different emission and absorption coefficients.

Under these assumptions, the rate equation for the population in excited state N2 and the

photon propagation equation are [36]:

33

2 2

10

2

( , ) ( , ) 1 ( , )

( , )( , ) ( , )

Ni

i

it eff

nn n n n n

N z t N z t P z tu

t N A z

P z tu N z t P z t

z

(2.21)

The γn and αn are emission and absorption constants defined as:

e

n t n n

a

n t n n

N

N

(2.22)

N2(z, t) is the fractional population of the upper state. Pi(z, t) is the optical power of the

pumping and/or signals, in units of number of photons per unit time. Nt is the doping

concentration of Er ions. Aeff is the effective fiber core area. τ0 is the life time of the

upper state population. Г is the overlap factor. σe and σ

a are the emission and absorption

cross sections for a specific wavelength. u is the unit vector, for forward direction u= +1,

for backward direction u= -1.

34

Figure 2.9 An example of the transient response. Inset shows the same transient response

over a long time period. Δt expresses the time span for changing the gain by 0.5 dB from

the initial value after changing the input channel number [37].

Figure 2.9 is an example of dynamic gain with channel add-on using Equations 2.21 and

2.22 [37]. As shown in Figure 2.9, the simulations for transient gains deal with the

signals varying in the μs range. The signals in the DANTEEO system vary in the ns range,

as shown in Figure 2.8. The red rectangle in Figure 2.9 represents the time window that

we are interested in as the signals in the DANTEEO system always change amplitudes in

a very fast way. We will apply this model (Equation 2.21) in the simulations of transient

gains for fast signals with amplitudes changing in the ns range in Chapter 4.

The region we

are interested

35

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30. O.K. Lim, V. S. Grigoryan, M. Shin, P. Kumar, “Ultra-low-noise inline fiber-optic

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35. R. M. Jopson and A. A. M. Saleh, “Modeling of gain and noise in erbium-doped

fiber amplifiers,” SPIE Fiber Laser Sources and Amplifiers III, vol. 1581, pp. 114–119,

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36. Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average Inversion Level, Modeling and

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38

Chapter 3: Erbium-doped fiber amplifiers (EDFAs) for

NIF DANTE system

In this chapter, we will describe the EDFA configurations for low noise NIF DANTEEO

system diagnostics. The comparison of different EDFA setups will be discussed based on

noise levels and the pulse shape restoration.

3.1 EO diagnostic system for NIF DANTE (NIF DANTEEO)

3.1.1 The EO system configuration

This EO data acquisition system is built to enhance SNR so that it can be a viable

alternative to the current system. The whole system is packed in a black box for system

stability and low noise. The picture is shown in Fig 3.1. The configuration of the EO

system is shown in Fig 3.2, followed by the detailed description of the system.

Figure 3.1 NIF DANTEEO system packed in a black box.

39

3.1.2 System specifications of the components

A four channel DFB laser (from Optilab) is used as the source laser. The wavelength of

each channel is tunable within some range. The tuning step is 0.2nm. The details are

listed in Table 3.1.

Table 3.1 Parameters for the DFB laser

Channel Output Power (dBm) Wavelength (nm) Wavelength Tuning Range (nm)

Ch. 1 12.34 1547.73 1546.12 – 1549.65

Ch. 2 12.19 1552.52 1550.92 – 1554.15

Ch. 3 12.77 1554.13 1552.41 – 1555.72

Ch. 4 16.40 1557.35 1555.65 – 1558.93

The actual wavelength from the laser has a little deviation from the panel readout. If the

output power is changed the output wavelength will change as well. So the wavelengths

we noted on this proposal are the wavelengths we measured with a calibrated spectrum

analyzer.

The configuration of the DANTEEO system is in Figure 3.2. The detailed explanation

follows:

All laser wavelengths come from a four channel CW DFB laser system. PC represent in-

line polarization controller. AOM represents an acoustic optical modulator. MZ

represents Mach-Zehnder modulator.

40

(a)

(b) (c)

Figure 3.2 The schematic of the EO system for NIF DANTE (a). The thick black arrows represent electrical signals and the

thin black arrows represent optical signals. Schematics of 4× (b) and 2× (c) replicator used in the DANTE system shown in (a).

40m

200ns 80m

400ns 20m

100ns

41

90/10 is the beam splitter, in which 10 percent of the input light is used as a feedback for

the MZ bias-dithering, control system and the remaining 90 percent of the input light

goes to DWDM component. RF is the radio frequency signal from an electronic signal

generator which is used to drive the Mach-Zehnder. The 1×3 splitter is the one input and

three output RF connector. OSC Chan is the channel of the oscilloscope. EDFA is the

commercial EDFA with details described later in this chapter. Replicator is a fiber

replicator using the delay line configuration to create identical copies of the input pulses.

There are total three output ports of this 8× fiber replicator. One port connected to

detector #1 is from the 4× replicator, so the output will be four pulses for each

wavelength. Another 4× output was connected to a 2× input port on panel. The other

output from the 4x replication stage was connected to Detector #1 which was a DSC

402DC photodetector with amplification. One of the outputs of the 8x replication stage

was connected to Detector #2 which was a DSC 50S photodetector without any

amplification.

The optical paths for both 1557nm and 1552nm were almost the same except that

1552nm had a delay line before the DWDM wavelength combiner. First, the AOM carves

the CW laser output into a 100 ns pulse with a repetition rate of 39 Hz. This repetition

rate was chosen much less than the 1-kHz dither frequency to stabilize the MZM. The

Mach-Zehnder imprints the signal to be measured onto the square pulse into a window

about 30ns wide at the top of the square pulse. The AOM has high extinction ratio so that

it can create a clear background with zero intensity beyond the signal. This high

extinction ratio is needed to propagate the pulses through the replicator without optical

42

interference. However, the AOM suffers from a rather long arise time (15 ns), which

forces a minimum time window of about 50ns for the signals in the DANTEEO system.

The Mach-Zehnder modulator has lower extinction ratio, however it has a high

bandwidth (up to 10 GHz). As our system is designed for signals up to 6GHz, the MZ

modulator provides sufficient bandwidth margins for all the measurements the system

will make. So the AOM and MZ are combined to create low background, fast optical

pulses. As the efficiency of pulse carving of the Mach-Zehnder modulator is related to

the polarization, a polarization controller and a polarizer were installed before the MZ to

get maximum modulation. The delay line added in 1552nm optical path was used to

avoid temporal overlap of two wavelengths in the fiber replicator.

Due to the long rise time of the first AOM that was used (about 40ns), the original system

was designed for signals with time width about 160ns. So the 4× replicator (shown in

Figure 3.2(b)) was built for about a 200ns time window. A faster AOM (about 15ns arise

time) was used in the later experiments, which can narrow the signal time window to

about 60ns. Accordingly, we built another 2× replicator as shown in Figure 3.2(c). One

output of the 4× replicator was connected to the input of the 2× replicator. Together with

4× replicator, this replicator combination can create total 8 duplicate signals with 100ns

time window.

The commercial EDFA needs a CW input of about 1mW, otherwise it will turn-off

automatically. So the third wavelength, 1547nm, is used to keep the commercial EDFA

active before the signal pulse train arrives. The output #2 of the replicator shown in

43

Figure 3.2 was left unconnected in the original system. The EDFA developed for this

thesis used this output to monitor the pulse shape differences between the input and

output of the EDFA.

The DWDM component used in the EO system was a 200GHz-spacing 8-channel

multiplexer. The operating wavelengths for each channel were 1547.72nm, 1549.32nm,

1550.92nm, 1552.52nm, 1554.13nm, 1555.75nm, 1557.36nm and 1558.98nm.

Figure 3.3 Schematic of commercial Mach-Zehnder bias controller [1].

Figure 3.4 Calibration of both MZ modulators.

44

The MZ modulators use the electro-optic effect to modulate the phase of the incoming

light. And therefore, they are very sensitive to environmental conditions such as

temperature and stress. To ensure a stable bias point in the transmission curve and a

stable pulse shape output, a commercial Mach-Zehnder bias controller was used to

maintain the optical bias at the negative quadrature point. Similar to the commercial

EDFA, the MZM bias controller also needs a CW signal because the dither controller

assumes harmonics of the dither frequency are always on. The schematic illustration is

shown in Figure 3.3. This extra CW signal channel plays an important role in the system

because it affects the gain dynamics of EDFAs, which will be discussed in section 3.3.3.

To apply MZM in the DANTEEO system, Vπ of both Mach-Zehnder modulators was

carefully calibrated. The calibration process was done through the measurement of

transmitted light intensities (transmission) versus the applied voltage. The results are

shown in Figure 3.4.

As we mentioned in Chapter 2, the fiber replicator will distribute the optical power into

several nearly identical. The amplitude of the output signal (for example, at output #2 in

Figure 3.2) was too small to be detected with a standard photodiode. Although the SNR

can be enhanced by averaging the identical pulses, the overall SNR will suffer from weak

signals because the SNR is proportional to the signal power. So we need an amplifier to

provide enough gain to measure the signal without introducing too much noise [1]. In the

DANTEEO system, an amplified photodetector was used after the 4× replicator to

amplify the signals electronically. However, this detector did not provide enough gain to

make measurements with a SNR of at least 100. We need an optical signal amplifier to

45

get amplified analog optical signals as it is hard to estimate the analog pulse-shape

distortion from amplified photodetectors. An EDFA was used in the DANTEEO system

to amplify signals beyond the noise floor of the photodiodes. The EDFAs can amplify

signals within large wavelength range (about 40nm) in telecomm band. They have low

noise and high output powers. The maintenance of EDFAs is also comparatively easy as

they do not demand complicated alignment techniques.

We have both C-band and L-band Erbium-doped fibers in lab. The L-band Erbium-doped

fibers came from Thorlabs. The C-band Erbium-doped fibers came from 3M, the

absorption and emission cross sections are shown in Figure 3.5. We will use the

estimated absorption and emission cross sections based on parameters from this figure to

calculate the dynamic gain in Chapter 4.

1450 1500 1550 1600 1650-1

0

1

2

3

4

5

6

7

8

Wavelength (nm)

Inte

nsity (

dB

/m)

Absorption Coefficient

Emission Coefficient

Figure 3.5 Absorption and emission coefficients in the C-band Erbium-doped fiber [2].

46

3.2 Characterization of the commercial EDFA

In order to exceed the noise and gain performance of the current commercial EDFA

(MANLIGHT), we took a set of data with different pumping laser currents in the unit of

mA [1]. The parameters of this commercial EDFA are listed in Table 3.2.

Table 3.2 Parameters of the commercial EDFA [1].

Parameters Specification Unit

Pump Laser Wavelength 975 nm

Pump Laser Power 300 mW

Pump Laser current for 20 dBm Output power 471.0 mA

Amplifier Gain 5-30 dB

Saturated Output power 20 dBm

Figure 3.6(a) is the 4× pulse train with the photodetector (DSC403DC) which has a gain

M = 2-7. The amplified photodetector was used to monitor the system and also to

compare with the optical amplified signals (the signals out of this detector are electrically

amplified). Figure 3.6(b) is the 8× pulse train from the commercial EDFA amplified with

a pumping laser current of 90mA. This is the small signal gain regime where the EDFA is

unlikely to introduce pulse shape distortions. The inserted small plots on the upper right

corner of Fig 3.6(a) and (b) are the individual pulses. The dynamic range (DR) is defined

as the ratio between the largest and the smallest signal amplitudes. The dynamic range in

Figure 3.6(b) for the commercial EDFA pumped with 90mA is about 6, far away from

47

system design requirements (above 4000). The low dynamic range and low SNR as well

should be attributed to weak signals and noise from the amplifier.

1200 1400 1600 1800 2000 2200 2400-0.005

0

0.005

0.01

0.015

0.02

0.025

Time (ns)

Am

plit

ud

e (

V)

(a)

1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 32000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Time (ns)

Am

plit

ud

e (

V)

(b)

Figure 3.6 The pulse trains from 4× output with an amplified photodetector (a) and 8×

output amplified by the commercial EDFA with 90 mA pumping current (b).

1160 1170 1180 1190 1200 1210 1220 1230-0.005

0

0.005

0.01

0.015

0.02

0.025

Time (ns)

Am

plit

ud

e (

V)

1340 1350 1360 1370 1380 1390 14000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

Time (ns)

Am

plit

ud

e (

V)

48

As all components of the commercial EDFA were sealed in the black box, the only way

to enhance the SNR and dynamic range was to get higher amplification. To increase the

amplification, the pumping laser current of the EDFA was increased. The results were

recorded using a digital oscilloscope. As the working conditions of the laser source and

the Mach-Zehnder modulators may vary with time, the actual optical powers of the input

and amplified signals will also vary. So the ratio between the maximum amplitude of the

amplified signals and the 4× output signals as recorded on the DSC 403DC photodiode

was used to characterize the amplification of the commercial EDFA.

80 100 120 140 160 180 2000

0.5

1

1.5

2

2.5

3

3.5

4

Pumping Current (mA)

Am

plit

ud

e R

atio

Figure 3.7 The relationship between the amplitude ratio between 4× output signals and

the EDFA pumping current. Curves come from two different measurements.

We measured the output powers of the EDFA with the pumping laser currents from 90

mA to 190 mA (190 mA is the maximum pumping current set for the experiments to

49

avoid gain saturation). For each pumping current, we measured 10 times with 1 min

separation in time. The amplitude ratio in Figure 3.7 is the average of the ratio between

the optically amplified signals and the electrically amplified signals. The black and blue

curves in Figure 3.7 come from two measurements (at different days) with different

Mach-Zehnder RF voltages. From this figure, the amplification of the commercial EDFA

is quite stable. The EDFA gain is linearly proportional to the pumping current.

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 30000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (ns)

Am

plit

ud

e (

V)

Figure 3.8 The amplified signals with the pumping current at 190 mA.

50

0 10 20 30 40 50 60

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

GPIBczha

Built-in EDFA 190mA

2.hdf MZ 1

Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 600

50

100

150

200

250

300

350

400

GPIBczha

Built-in EDFA 190mA

2.hdf MZ 1

Time (ns)

SN

R

(b)




calculated SNR vs. time corresponding to the pulses in (a).

Background level

51

0 10 20 30 40 50 60

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

GPIBczha

Built-in EDFA 190mA

2.hdf MZ 2

Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 600

50

100

150

200

250

GPIBczha

Built-in EDFA 190mA

2.hdf MZ 2

Time (ns)

SN

R

(b)




calculated SNR vs. time corresponding to the pulses in (a).

Background level

52

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-70

-60

-50

-40

-30

-20

-10

Wavelength (nm)

Inte

nsity (

dB

m)

Figure 3.11 The spectrum of the amplified signals shown in Figure 3.8. The ASE

background is continuous. The duty cycle for the holding channel is about 100%, for two

signals channels (1552nm and 1557nm) is 6.6×10-3

%.

Figure 3.8 is the waveform reading from the oscilloscope. Figure 3.9(a) and Figure 3.10(a)

are the aligned pulses. For each set of pulses (8 pulses) in Figure 3.8, we aligned them

together and rescaled the pulses to have the same amplitude as the first pulse in each set.

Figure 3.9(b) and Figure 3.10(b) are the calculated SNR(t). The formula used to calculate

SNR is:

Avg V NSNR

Std V

(3.1)

Avg (V) is the averaged amplitude value of eight pulses, Std (V) is the standard deviation

at each point in time of all eight rescaled pulses, N is the number of replicas. Figure 3.9(b)

and Figure 3.10(b), the SNR for Mach-Zehnder #1 is about 150, for Mach-Zehnder #2 is

about 75. The background level is about 0.02 V. The amplification of the commercial

53

EDFA added extra CW background level of 0.02 V, about 8 μW. This CW background

mostly comes from ASE. The SNRs in Figure 3.9 and Figure 3.10 are the best SNRs that

can be achieved with this commercial EDFA without distortions. Figure 3.11 is the

spectrum. The three peaks are associated with the two signal wavelengths and the one

holding channel at 1547.72nm. The duty cycle of the holding channel is about 100%. The

duty cycle for the two signal channels is 6.6×10-3

%. The broadband background across

the whole spectrum can be attributed to ASE.

3.3 Characterization of EDFAs

This section describes a variety of EDFAs that were constructed as alternatives to the

commercial unit and discusses the relationship between the EDFA performance (gain and

noise) and a variety of component parameters.

3.3.1 EDFAs with L-band Er-doped fiber and multi-stage configuration

For a single stage EDFA, there are several different configurations including forward, bi-

direction and backward based on pumping schemes. In the DANTEEO system, the signal

to be amplified was very weak and barely able to be detected even with an amplified

photodetector. Therefore, based on simulations with commercial software shown in

Figure 2.6, a long Er-doped fiber was not needed. In other words, the amplification

depends on the power of the input signal, in a single-stage configuration. Besides, the

54

noise or the SNR is also proportional to the amplitude of the amplified signal. In order to

obtain high SNRs, we need high amplifications which are impossible for single-stage

configurations with very weak input signals. There are two choices available, a

regenerative EDFA or a multi-stage EDFA. The regenerative EDFA is similar to an all-

fiber ring laser configuration, in which an optical pulse circulates in a fiber cavity where

it efficiently gains energy by repeated passes in the gain fiber [3-10]. The advantage of

the regenerative EDFA is the high gain with compact size. However it has a relatively

high noise level as both signal pulses and the noise (mainly ASE) circulate and are

amplified in the loop. For the current DANTEEO system, we prefer high SNRs even at

the cost of lower amplification. So we chose another solution, the multi-stage EDFA.

Different multi-stage configurations were tried to decrease the noise. Generally speaking,

there are several sources of the noise. The most apparent source of the noise is ASE,

amplified spontaneous emission. Light originating from ASE has a spectrum

approximately the same as the gain spectrum of the Er-doped fibers which means the

ASE covers a wide wavelength range. The ASE has no fixed frequency in time domain

and no fixed phase relation relative to the signals. Therefore, ASE is very hard to remove

in phase-insensitive optical amplifiers like an EDFA. This kind of noise is random in

time and polarization. Another source of the noise is the EDFA pumping laser. The

population inversion in Er-doped fibers does not reach 100%, there are still some residual

powers from the 980 nm pumping laser at the output. As the pumping laser is CW, this

type of noise is CW and can be mostly eliminated by bandpass filters, or dropped off by

WDMs as shown in Fig 3.12 and 3.13. Another noise source comes from the bandwidth

55

of the photodetector, also called white noise. To reduce the white noise, the most efficient

method is to choose a photodetector with the bandwidth only a little larger than the signal

frequency in time domain. The signal frequency in our current DANTEEO system is 39

Hz, the bandwidth of our current detector is 10GHz. So if we choose a photodetector with

much lower bandwidth, we can increase the SNR dramatically. However, the

DANTEEO system is designed for finally up to 6GHz signals. So currently we ignore

this type of noise.

The inevitable noise, or the base noise, is the initial signal noise. Different configurations

of EDFAs are designed to decrease only the extra noise from the amplification process.

The noise from the original signal is amplified simultaneously along with the signal. So

the fiber replicator can actually increase and decrease the noise in this DANTEEO system.

It produces the replicas for mathematical averaging to increase the SNR. On the other

hand, the extra amplifier such as the EDFA has to be used to amplify the signal which

degrades the SNR. The final SNR, either improved or degraded by the fiber replicator,

depends on the competition between these two effects. So our target is to suppress the

noise introduced by the EDFA for the particular signal pulse train generated by the

DANTEEO system.

56

Figure 3.12 Two-stage dual forward pumping EDFA experimental setup.

Figure 3.12 is the two-stage dual forward pumping EDFA configuration. The BWDM

after the first stage was used as a filter to narrow the wavelength range. As the passing

band for the BWDM is 1554.89-1563.89nm, we used the BWDM to remove the ASE

background beyond the passing band. The residual powers from the 980nm pumping

laser after the first stage was deliberately neglected as this residual pumping power can

be used (or recycled) in the second stage amplification. The WDM after the second stage

was used to drop the pumping channel and the DWDM was used to further narrow the

bandwidth of the amplified signals. The signal wavelengths 1555.73nm and 1557.36nm

were specifically chosen that these two wavelengths were within the pass band of the

BWDM and were exactly the same wavelengths as two of the DWDM channels. The

pump power for the first stage was 60 mW and the second stage was 40.4 mW. The

pumping laser used in the lab to build the EDFAs described in this Chapter came from

Amonics Limited (980nm Benchtop FP Laser Source, Model: AFP-980-300-B-FA).

57

Table 3.3 Optical Parameters of the EDFA pumping laser [11].

Parameter Units Test Data

Centre wavelength nm 974.56

Output power @ centre wavelength mW > 290

FWHM nm 0.418

Output stability (over 8 hours) dB < ±0.02

Figure 3.13 Two-stage forward and backward pumping EDFA experimental setup.

There are three possible pumping schemes for two-stage EDFAs, dual forward pumping

(such as the EDFA configuration shown in Figure 3.12), forward and backward pumping

(such as the EDFA configuration shown in Figure 3.13) and dual backward pumping

schemes. As the individual pulses in the pulse train have different polarizations, the

polarization related components such as Faraday isolators are not applicable in the

DANTEEO system. In the fiber-optical systems, the Faraday isolator is used to allow the

transmission of light in only one direction and prevent the damages from unwanted

feedback light. In order to prevent the system damage from the backward traveling pump

light for the system without isolators, the backward pumping schemes for the first stage

58

were not considered appropriate in the DANTEEO system. The backward pumping

scheme can be used in the second stage because the first stage will deplete the excess

pump light from the second stage. Therefore, the final gain and noise performance were

critically dependent on the pumping scheme of the second stage. The forward pumping

scheme on the second stage, which occurs primarily near the input end of the Er-doped

fiber, has the characteristic of low gain and low noise level. While the backward

pumping scheme on the second stage, which occurs primarily near the output end of the

fiber, is supposed to be high gain and high noise level. This high noise level comes from

the strong backward ASE power at the output end of the fiber. These two different

configurations were tried to determine which one is better for the DANTEEO system.

Figure 3.14 - 3.20 are the experimental results and the calculated SNR distributions for

these two configurations.

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Time (ns)

Am

plit

ud

e (

V)

Figure 3.14 The amplified signals with the configuration shown in Figure 3.12.

59

0 10 20 30 40 50 600

0.02

0.04

0.06

0.08

0.1

0.12GPIB

czha

Forward pump with BWDM and DWDM 2.5m+5m

60mW+40.4mW6.hdf MZ 1

Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 600

50

100

150

200

250GPIB

czha



Time (ns)

SN

R

(b)




replicas. (b) The calculated SNR vs. time corresponding to the pulses in (a).

Background ≈ 0.005 V

60

0 10 20 30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08GPIB

czha



Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 600

20

40

60

80

100

120

140GPIB

czha



Time (ns)

SN

R

(b)





Background ≈ 0.005 V

61

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time (ns)

Am

plit

ud

e (

V)

Figure 3.17 The amplified signals with the configuration shown in Figure 3.13.

62

0 10 20 30 40 50 60-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16GPIB

czha

Forward pump with DWDM and WDM dropoff 2.5m+5m


Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 60

0

50

100

150

200

250

300GPIB

czha



Time (ns)

SN

R

(b)





Background

level

63

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04GPIB

czha



Time (ns)

Am

plit

ud

e (

V)

(a)

0 10 20 30 40 50 60

0

10

20

30

40

50

60GPIB

czha



Time (ns)

SN

R

(b)





Background

level

64

0 0.02 0.04 0.06 0.08 0.1 0.120

20

40

60

80

100

120GPIB

czha


60mW+40.4mW6.hdf

Amplitude (V)

SN

R

MZ1

MZ2

(a)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

20

40

60

80

100

120

140

160GPIB

czha


60mW+30.4mW3.hdf

Amplitude (V)

SN

R

MZ1

MZ2

(b)

Figure 3.20 Comparisons of the SNRs at different signal amplitudes (a) dual forward

pumping scheme, the configuration shown in Figure 3.12 (b) forward and backward

pumping scheme, the configuration shown in Figure 3.13. The dashed blue lines are the

fittings of the SNR vs. Amplitude. The dashed and point green lines in the two figures are

the SNR at the signal amplitude 0.1 V reading from the oscilloscope.

65

Figure 3.14-3.19 are the experimental results from the configurations described in Figure

3.12 and Figure 3.13. In Figure 3.20, the SNR vs. signal amplitude were plotted for two

different configurations. MZ1 and MZ2 in the Figure 3.20 represent the two signal

channels which were modulated by two individual MZMs, and shown in Figure 3.14 and

3.17 as two pulse trains (each has 8 duplicated pulses). From both plots in Figure 3.20,

the SNRs for the two signal channels agreed well with each other as the red and black

dots overlaps. When the signal amplitude equals 0.1V (corresponding to 2.5 mW), the

forward and backward configuration has higher SNR (above 100) than dual forward

configuration (about 90), which are shown as green dashed lines in Figure 3.20. For

small signals (about 0.03V, corresponding to 0.83mW), EDFAs with dual forward

configurations also have lower SNR. The background levels for both configurations are

around 0.005V, smaller than the commercial EDFA. As a whole, the backward and

forward configuration has better noise performance than both forward pumping schemes.

As shown in Figure 3.20, the SNRs are not uniform with the signal amplitudes. In Figure

3.20 (a), the SNRs for the signals with 0.1 V in amplitudes have a variation of ±15

around 90. The error bars of the SNR mostly come from the ASE, shot noise and

accidental environmental noise.

Besides the gain and noise performance, the pulse-shape fidelity during amplification

process is also an important factor in the EDFA design for the DANTEEO system.

66

150 200 250 300 350 400 450-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Am

plit

ud

e (

v)

Lab-built EDFA

Commercial EDFA

Figure 3.21 Comparisons of pulse shape with the signals amplified by two EDFAs.

Figure 3.21 is the comparison of two EDFAs. The amplitudes were both normalized to

1V to compare the pulse shape. The lab-built EDFA, shown as the black line, is the same

configuration in Figure 3.12 with the pump power at 75 mW for the first stage and 18

mW for the second stage. The commercial EDFA, shown as the red line was pumped at

180 mA. From this figure, we can find two major problems for the commercial EDFA.

The pulse was broadened during amplification process. And the commercial EDFA did

not do well with analog signals that have high frequencies. The high frequency is

typically defined as being equal to 0.33/Δt where Δt is the temporal structure of interest.

We found the amplified pulses from the commercial EDFA have the uniform pulse

shapes with those from lab-built EDFAs and amplified photodetectors while below

130mA (the gain is about 2-5 dB). Above 130mA pumping current, the pulses from the

commercial EDFA started distorting such as those shown in the Figure 3.21.

67

For different configurations and fiber components we tried in the experiments, we found

that

We cannot use polarization related fiber optics in our setup such as isolators.

Because the individual pulses in the pulse train have different polarizations, the

polarization related optics cannot modulator the individual pulses evenly.

For the above reason, backward pumping cannot be used in a one-stage

configuration, or in the first stage of a two-stage configuration. But the backward

pumping in the second-stage of a two-stage configuration as shown in Figure 3.13

can increase the SNR without introducing strong backflow of energy toward the

MZM‟s.

Because the Er-doped fiber has wide amplification spectrum, the output signal

after the EDFA has much wider spectrum than the input signal. In addition, there

is typically some residual pump light present at the output of the Er-doped fibers.

Bandpass filters can increase the SNR and largely decrease the background level.

In the two configurations in Figure 3.12 and 3.13, either a WDM after the second-

stage was used to remove the residual pump light or a backward pumping scheme

was used to decrease the pump light reaching the photodiode. BWDM and

DWDM spectral filters were used to narrow the spectrum of the signal and rule

out the noise.

Compared with the commercial EDFA, the constructed EDFAs have two

advantages, lower background and higher pulse-shape fidelity. Under the similar

amplification, our EDFAs have about ¼ the background level (0.005 V,

68

corresponding to 0.125 mW) of the commercial EDFA (0.02 V, corresponding to

0.5 mW). Besides, the commercial EDFA has pulse-shape distortions under large

amplification (above pumping current at 130 mA) for the pulses with high

frequencies (such as the pulses shown in Figure 3.21). By comparison, our lab

EDFAs do not have obvious pulse-shape distortion even under the highest

amplification and with signals having high modulation frequencies.

3.3.2 Performance of EDFAs with L-band and/or C-band Er-doped fibers

The previous section emphasized on the effect of different configurations on the gain and

noise performance of EDFAs. The Er-doped fibers used in the previous experiments were

all L-band Er-doped fibers from Thorlabs. This chapter will focus on the effect of

different Er-doped fibers (C-band and L-band) with different material properties on the

gain and noise performance of EDFAs.

Figure 3.22 Two-wavelength pulse trains were generated via AOMs to simulate the

electro-optic measurement system input to the EDFA.

69

For simplification, an acousto-optic modulator (AOM) was used to generate the pulse

train for each wavelength. The setup configuration is shown in Figure 3.22. The two

pulse-trains from two different wavelengths have a time separation length about the time

length of a whole pulse train to prevent the crosstalk. A DWDM was used to combine

two signals.

To compare the effect of C-band and L-band fibers on EDFA performance, a simple one-

stage forward pumping configuration, as shown in Figure 3.23, was used. The pumping

wavelength was 980nm and the second WDM was used to drop off the residual pumping

power.

Figure 3.23 A single-stage EDFA configuration for testing different types of optical fiber.

70

1400 1600 1800 2000 2200 2400 26000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (ns)

Am

plit

ud

e (

v)

C-band Er-doped fiber with 25mW pumping

Figure 3.24 Signals from a single-stage EDFA with C-band Er-doped fibers. The typical

waveform read directly from the oscilloscope, the pump power is 25mW at 980nm.

Background

level

71

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-70

-65

-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

40mW

35mW

30mW

25mW

20mW

15mW

10mW

7mW

(a)

1545 1550 1555 1560-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

40mW

35mW

30mW

25mW

20mW

15mW

10mW

7mW

(b)

Figure 3.25 The spectra for EDFAs with C-band Er-doped fibers (a) with different

pumping powers (b) zoom-in the spectra at signal wavelengths from 1545nm-1560nm.

The length of the C-band Er-doped fiber in Figure 3.24 is 3-meter. The input signals were

about -44 dBm (1547nm) and -42dBm (1557nm). The repetition rate is 39 Hz. Two

sharp peaks (at 1547nm and 1557nm) in the spectra (Figure 3.25) were the signal

72

wavelengths. From the oscilloscope waveform, the background is about 0.034 V and the

dynamic range is less than 7:1. A WDM was used to remove the residual 980nm pump

light. The background and the noise level should be mostly attributed to the strong ASE.

Figure 3.25 show the spectra at the output. With the increase of the pump power, the

spectral background and the amplitudes of the ASE peaks around 1530nm also increase.

Although the spectral data were recorded with the pump power to 40mW, the waveform

data was only recorded up to pump powers of 26mW. Above that level, the ASE signals

were too strong and the photodetector were saturated. A nonlinear effect, presumably

excited-state absorption, was observed with high pump powers (about 200mW and

above). There was, very obviously, green light coming out of the EDFA in this situation.

73

1600 1800 2000 2200 2400 2600-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Time (ns)

Am

plit

ud

e (

v)

L-band Er-doped fiber with 100mW pumping

(a)

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

140mW

120mW

100mW

80mW

60mW

40mW

(b)

Figure 3.26 Signals from single-stage EDFA with the L-band Er-doped fiber. (a) The

typical waveform reading from the oscilloscope, pump power is 100mW. (b) The spectra

under different pump powers. The red circle shows the spectral hole burning (SHB).

Figure 3.26 are the oscilloscope waveform and the spectra of a 4.5-meter L-band Er-

doped fiber single-stage EDFA. Compared with the C-band Er-doped fiber, EDFAs with

SHB

Background level

74

L-band Er-doped fibers had much lower background (≈0.02 V, corresponding to 0.5 mW)

and higher dynamic range (≈ 12:1). However, increasing the pump power for higher gain

resulted in spectral hole burning (SHB) [11]. As shown in Figure 3.26, the SHBs are

located at about 1554nm and the amplitude is about 0.5 dB with 140mW pump power.

The gain between 1547nm-1560nm becomes flatter with the increasing pump power up

to about 120mW. The peak of the gain around 1530nm also moves very slightly toward

(less than 0.5nm, almost invisible in the zoom size of the spectra plots in the thesis)

shorter wavelengths with increasing pump powers. By comparison, the peak of the gain

around 1530nm in the EDFAs with C-band Er-doped fibers did not move with the change

of the pump powers. The EDFA with the L-band Er-doped fiber also has gain

compression around 1540nm which might come from the gain saturation around 1530nm

[12]. The magnitude of the gain compression is nearly independent on the pump power.

By comparison, the EDFA with C-band Er-doped fibers does not have obvious gain

compression.

75

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

L-band 4.5m Er-doped fiber pumping with 80mW

C-band 3m Er-doped fiber pumping with 25mW

(a)

1540 1542 1544 1546 1548 1550 1552 1554 1556 1558 1560-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

L-band 4.5m Er-doped fiber pumping with 80mW

C-band 3m Er-doped fiber pumping with 25mW

(b)

Figure 3.27 The comparison of C- and L- band Er-doped fibers. (a) The whole spectra

range from 1500nm to 1600nm. (b) Spectra around 1540nm to 1560nm.

Figure 3.27 are the comparisons of the spectra obtained with two different types of Er-

doped fibers. The spectra for comparing the Er-doped fibers were taken at moderate gains

(about 15-25 dB depending on different types of Er-doped fibers). The spectrum analyzer

76

measures the CW optical power, so it does not accurately reflect the gain of the transient

signals. However, useful information can still be gathered from this instrument. The

EDFA with C-band Er-doped fibers had much higher ASE background, about 10 dB

higher in short wavelengths (around 1510nm) and 3dB in long wavelengths (1590nm).

However the peak of its ASE gain (around 1530nm) was much weaker than L-band Er-

doped fibers. From this point of view, the filter included in the single stage EDFA (as

shown in Figure 3.23) will work more efficiently with L-band Er-doped fibers in

removing the ASE background. This is because the ASE gain spectrum is concentrated

far from the signal wavelengths. Also, the L-band Er-doped fiber has a much flatter gain

within the band of interest (1547-1559 nm) than the C-band Er-doped fiber. However the

L-band Er-doped fiber experiences the SHB at about 1554nm (the affected wavelengths

range from 1553nm to 1554.5nm), which is actually one of the ITU-200 channels used at

the DANTEEO system.

77

1600 1800 2000 2200 2400 2600-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (ns)

Am

plit

ud

e (

V)

L-band +C-band Er-doped fiber with 100 mW pumping

(a)

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-70

-65

-60

-55

-50

-45

-40

-35

-30

-25

Wavelength (nm)

Am

plit

ud

e (

dB

m)

120mW

100mW

80mW

60mW

40mW

(b)

Figure 3.28 Signals from the single-stage EDFA with L-band + C-band Er-doped fiber. (a)


spectra for different pump powers.

Figure 3.28 includes the signal waveform and spectra from an EDFA with both L-band

and C-band Er-doped fibers. The two types of Er-doped fibers were directly connected

together via fiber connectors. The signals went through the L-band Er-doped fibers first

Background level

78

and then followed by the C-band Er-doped fibers. From the spectral plots, this type of

mixed Er-doped fibers had characteristics that are the sum of individual fibers, such as

gain compression around 1540nm, gain slope from 1542nm and flattened gain between

1550nm and 1557nm. From the oscilloscope waveform, this mixed fiber is closer to the

C-band fiber with its characteristics of high gain and high noise.

79

1600 1800 2000 2200 2400 2600-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time (ns)

Am

plit

ud

e (

v)

C-band + L-band Er-doped fiber with 100mW pumping

(a)

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-80

-70

-60

-50

-40

-30

-20

Wavelength (nm)

Am

plit

ud

e (

dB

m)

120mW

100mW

80mW

60mW

40mW

(b)

Figure 3.29 Signals from single-stage EDFA with C-band + L-band Er-doped fibers. (a)


spectra with different pumping power. The blue circle illustrates the spectral

characteristic of parasitic oscillations.

Figure 3.29 includes the signal waveform and the spectra from an EDFA with both C-

band and L-band Er-doped fibers. The Erbium gain medium was also composed of a

Background level

80

directly connected two types of Er-doped fibers. This configuration is different from that

shown in Figure 3.28, in that the C-band fiber came first and followed by the L-band Er-

doped fiber. The signal waveform is closer to an L-band Er-doped fiber with its low noise

and moderate gain. Comparing the spectra of the two types of mixed Er-doped fibers, the

C+L type has high ASE gain (around 1530), steeper gain spectra in the 1547-1559nm

band and exhibits SHB with high pump powers. The C+L type also had lower

background level (≈ 0.02 V, corresponding to 0.5 mW) than the L+C type (0.05V,

corresponding to 1.25 mW). The 1530nm gain peak under 120mW was rather noisy, as

shown in the blue circle in Figure 3.29(b). This phenomenon probably came from the

parasitic oscillations within the C-band Er-doped fiber due to the reflections from the end

faces. As the experiments shown in the initial part of this Chapter, the C-band Er-doped

fiber has very low threshold pumping power (about several mW) compared with the L-

band Er-doped fiber. When the 120mW pump power was launched into the C-band Er-

doped fiber, both the signal and the ASE (especially the ASE peak wavelength of

1530nm) undergo signification amplifications. Because of the Fresnel reflections of the

fiber ends, the fibers will become a gain cavity for ASE signal oscillations. The

oscillation frequency will be different from that of the signals. So if the oscillation signals

are strong enough, the spectrum will have a modulated characteristic as illustrated in the

blue circle of Figure 3.29(b). The parasitic oscillations also affect the oscilloscope

waveform as seen by a second signal at a different modulation frequency from the 39Hz

trigger, as shown in Fig 3.30. This signal oscillates asynchronously with the triggered

81

signal that triggers the oscilloscope. This phenomenon occurs very frequently in single-

stage EDFAs with backward pumping schemes.

0 50 100 150 200 250 300 350 400

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Time (us)

Am

plit

ud

e (

V)

Figure 3.30 Free running ASE signals. The left small plot is the corresponding spectral

measurement.

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

Wavelength (nm)

Inte

nsity (

dB

m)

Real Signals

ASE Signals

82

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

2.5m C-band + 3m L-band Er-doped fiber with 80mW pumping

2.5m C-band + 3m L-band Er-doped fiber with 60mW pumping

3m L-band + 2.5m C-band Er-doped fiber with 80mW pumping

3m L-band + 2.5m C-band Er-doped fiber with 60mW pumping

(a)

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

Wavelength (nm)

Am

plit

ud

e (

dB

m)

4.5m L-band Er-doped fiber pumping with 80mW

3m C-band Er-doped fiber pumping with 25mW

3m C-band + 2.5m L-band Er-doped fiber pumping with 80mW

2.5m L-band + 3m C-band Er-doped fiber pumping with 80mW

(b)

Figure 3.31 Comparisons of the EDFA gain spectrum using different Er-doped fibers.

Figure 3.31(a) is the comparison of two different types of mixed fibers. From this plot

and the waveforms in the previous pictures, the gain of the mixed fiber seems to be the

weighted average of the constituent fibers with the first fiber that the signal is launched

83

into having the greatest weight. The noise performance seems dominated by the end fiber.

Compared with the L+C mixed fiber, the C+L fiber has lower gain and lower noise as its

ASE gain spectrum is more concentrated and lower than the C+L type. In the C+L

configuration, the L-band fiber works like a weak filter which lowers the gain of the

spectral wings. The combination of fiber lengths and pump powers illustrated in Figure

3.31(b) are the best choices of all four types of the Er-doped fiber configurations used in

a single-stage forward pumping EDFA.

Based on these experiments, the C-band fiber has the highest gain and the highest noise,

the L-band fiber has lower gain and the lowest noise, the C+L fiber has moderate gain

and moderate noise, and the L+C fiber has moderate to high gain and moderated to high

noise. The L+C configuration seems to be a good choice for the DANTEEO system.

Additional experiments were done to extend the single-stage EDFA results into the

double-stage EDFA configuration. The spectra of double-stage EDFAs are very close to

the spectra of single-stage EDFAs. For example, the spectrum of a double-stage EDFA

with L-band Er-doped fibers in the first stage and second stage is very close to the single-

stage EDFA with only L-band Er-doped fiber. Very good gain and noise performance

were obtained with a double-stage EDFA having the C-band Er-doped fiber in the first

stage and the L-band Er-doped fiber in the second stage. The waveform is shown in

Figure 3.32. We used a 15dB attenuator after the original signals (as shown in black in

the Figure 3.2) to reduce the signals into the levels similar as those coming out of the

replicator. About 30dB of amplification was obtained with moderate pump powers (about

84

80 mW forward pumping for the first stage and 60 mW backward pumping for the

second stage).

200 300 400 500 600 700 800 900 1000-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (ns)

Am

plit

ud

e (

v)

Original Signal (-15dB)

Amplified Signal

Figure 3.32 The oscilloscope waveform for a double-stage EDFA with C+L configuration.

The two pulse trains (either in black or in red) come from different wavelengths.

3.3.3 The addition of a holding channel and its effect on EDFA spectrum

As we can find from almost all spectra in the previous sections, there exists the effect of

gain saturation by ASE signals (around 1530nm). The gain coefficient of a

homogeneously broadened gain medium can be expressed as [14]:

0

2 2

21 /a s

gg

T P P

(3.2)

g0 is the peak value, ω is the frequency of the light, ωa is the atomic transition frequency,

P is the optical power of the signal and Ps is the saturated power. From this equation, the

85

value of the gain coefficient will decrease when the signal is close to saturation. So the

gain saturation actually limits the energy-extraction efficiency [15].

In order to surpass the gain saturation from ASE, a channel with a quasi-CW signal was

added (referred to as the “holding channel”). Then a large amount of inverted population

was used to amplify the holding channel, in a controllable configuration, before the gain

can be saturated by the ASE.

0 0.5 1 1.5 2 2.5 3

x 10-6

0

0.5

1

1.5

2

2.5

3

3.5

Time (s)

Am

plit

ud

e (

a.u

.)

Holding Chanel: 1547.8nm

Leading Chanel: 1557.4nm

Trailing Chanel: 1552.6nm

Figure 3.33 Waveforms of holding and signal channels used in the electro-optic data

acquisition system.

Figure 3.33 are the temporal profiles of three channels in the DANTEEO system. Red

and blue lines are the two signal channels with different wavelengths (1552.6nm and

1557.4nm). The black line shows the holding channel. When there were no EO signals,

the holding channel was “on”; while the EO signal carrier pulses were “on”, the holding

channel was turned off to prevent crosstalk with the signal channels. The “on and off”

Amplitude of the

holding channel

86

status of the holding channel was controlled through a MZM which couples a polarizer in

its input. For simplification, a polarization controller was added before the MZM to

adjust the amplitude (optical power) of the input light after the polarizer. The polarization

controller gave a coarse control of the optical power of holding channel.

1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600-70

-60

-50

-40

-30

-20

-10

Wavelength (nm)

Inte

nsity (

dB

m)

Without 1547.72nm channel

minimum power of 1547.72nm channel

maximum power of 1547.72nm channel

Figure 3.34 The gain spectra of the signals as a function of the holding channel power.

The amplitude of the ASE peak decreased with the increasing of the holding channel

powers, as shown in Figure 3.34. The gain through 1547nm to 1559nm band is flatter.

Further increasing of the power of the holding channel would decrease the ASE peak so

that gain saturation by ASE can be avoided.

87

Reference

1. W. R. Donaldson, C. Zhao, L. Ji, R. G. Roides, K. Miller, B. Beeman, “A single-shot,

multiwavelength electro-optic data-acquisition system for ICF applicationsa”, Review of

Scientific Instruments, vol. 83, No. 10, Oct 2012.

2. 3M datasheets for C- and L-band fibers with part number FS-ER-7A28 and FS-ER-

7B28.

3. A. Zavatta, J. Fiurasek and M. Bellini, “A high-fidelity noiseless amplifier for quantum

light states” , Nature Photonics. vol. 5, pp.52-60, 2011.

4. S.K. Choi, M. Vasilyev and P. Kumar, “Noiseless optical amplification of images”,

Phys. Rev. Lett, vol. 83, pp.1938–1941, 1999.

5. W. Imajuku, A. Takada and Y. Yamabayashi, “Low-noise amplification under the 3

dB noise figure in high-gain phase-sensitive fibre amplifier”, Electron. Lett, vol. 35,

pp.1954-1955, 1999.

6. K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on

symmetric-pump phase-sensitive amplification”, IEEE Photon. Technol. Lett, vol. 19, pp.

864-866, 2007.

7. O.K. Lim, V. S. Grigoryan, M. Shin and P. Kumar, “Ultra-low-noise inline fiber-optic

phase-sensitive amplifier for analog optical signals”, in Proceedings of the Optical Fiber

Communications Conference (OFC/NFOEC 2008), San Diego, USA, paper OML3, 2008.

8. R. Tang, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-

optic parametric amplifier with phase self-stabilized input”, Opt. Express, vol. 13, pp.

10483-10493 2005.

9. J. Kakande, “Detailed characterization of a fiber-optic parametric amplifier in phase-

sensitive and phase-insensitive operation”, Opt. Express, vol. 18, pp. 4130-4137, 2010.

10. Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J.

Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda and L. Grüner-Nielsen, “Towards

ultrasensitive optical links enabled by low-noise phase-sensitive amplifier”, Nature

Photonics, vol. 5, pp.430-436, 2011.

11. Amonics Limited, User‟s Manual for 980nm Benchtop FP Laser Source, Model:

AFP-980-300-B-FA.

12. Maxim Bolshtyansky, “Spectral Hole Burning in Erbium-Doped Fiber Amplifiers”,

Jounal of Lightwave Technology, vol. 21, No. 4, Apr 2003.

88

13. M. Tachibana, R. I. Laming, P. R. Morkel and D. N. Payne, “Gain cross saturation

and spectral hole burning in wideband erbium-doped fiber amplifiers”, Optics Lett, vol.

16, No. 19, Oct 1991.

14. P. W. Milonni and J. H. Eberly, “Lasers”, Wiley New York, 1988.

15. G. P. Agrawal, “Applications of Nonlinear Fiber Optics”, Academics Press, 2001.

89

Chapter 4: Numerical simulations of transient gains for

EDFAs in the DANTEEO system

This chapter presents a simplified model for the dynamic gain in an EDFA [1]. Because

the signals in the DANTEEO system are analog signals, the temporal profile of the gain

is also of interest. If the gain is not temporally uniform, the pulse shape fidelity will

decrease during the amplification process.

4.1 Simulation method

As stated in Chapter 2 section 2.2.5, the Equations set 4.1 (the same as Equation 2.21 in

section 2.2.5) should be used to calculate the transient gain. The first equation in

Equation 4.1 is a rate equation. The first term on the right side of the equation describes

the effect of spontaneous emission related to the population in the excited-state, while the

second term describes the effect of total optical power related to the inverted population.

2 2

10

2

( , ) ( , ) 1 ( , )

( , )( , ) ( , )

Ni

i

it eff

nn n n n n

N z t N z t P z tu

t N A z

P z tu N z t P z t

z

(4.1)

The second equation in Equation 4.1 is the light propagation equation, which has been

largely simplified by Saleh from its original complicated style including sets of coupled

partial differential equations [2-3]. The equation assumes “n” simultaneous optical

90

channels in the EDFA. The pump light is also regarded as an optical channel. From this

point of view, the pumping and the signals mutually affect the EDFA gain to the extent

that depends on their emission (γ) and absorption (α) coefficients, and the propagation

direction (u).

The finite difference method is used for numerical simulation. The signals are assumed to

only travel in the forward direction. Each time step permits only a very small propagation

length within the Er-doped fiber, for example 5mm per step. The transit time for 5mm

fiber is 25ps assuming the refractive index of the fiber is 1.5. Typical optical signals

change much more slowly (almost an order of magnitude slower). Under these

assumptions, the Equation 4.1 is applicable in the simulation of the DANTEEO system.

In the finite difference method, the signals were decomposed into segments in time

domain while the fiber was decomposed in space domain. For each small forward step

(Δz) in fiber, we will calculate the optical power for each small segment of the signal (Δt).

After going through a length of fiber equal to M×Δz for each Δt (the total length of the

pulse train is supposed to be N×Δt), we will reconstruct the signal and get the final

amplified signal. This process is shown in Fig 4.1. In the figure, a sequence of colored

boxes below the left original signal waveform represents the time segments Δt. The blue

boxes below the “Fiber” represent the length step Δz in fiber. The multiple arrays of

colored boxes below the right amplified signal waveform represent the amplified signals

for each time segment. The signal amplitudes after an EDFA are assumed to increase. So

we use more boxes in each Δt.

91

Figure 4.1 Schematic of the finite difference method in the calculation of the EDFA gain.

The numerical solution of the differential equations requires the boundary/initial

conditions for N2 (z, 0) and Pp (z, 0), assuming there are no signals launching in the fiber

at initial time. The initial conditions can be calculated through the steady-state solution of

the Equation set 4.1[4-5]:

2 2

0

2

,( , ) ( , ) 10

( , )( , ) ( , )

p

i

t eff

p

n n n n p

P z tN z t N z tu

t N A z

P z tu N z t P z t

z

(4.2)

The Equation set 4.2 assumes there is only one pumping source for each fiber. We also

assume there is no other light source propagating (signals) in the fiber. The “ui”

represents the direction of pumping which equals “+1” for forward pumping and “-1” for

backward pumping. The steady-state condition requires that the partial derivative of time

equals zero. Then the upper-state population can be calculated from the rate equation:

M×Δz

0 1000 2000 3000 4000 5000 60000

0.5

1

1.5

2

2.5

3

3.5

Time (ns)

Am

plit

ude (

a.u

.)

Holding Channel: 1547.8nm

Leading Channel: 1557.4nm

Trailing Channel: 1552.6nm

0 1000 2000 3000 4000 5000 60000

0.5

1

1.5

2

2.5

3

3.5

Time (ns)

Am

plit

ude (

a.u

.)

Holding Channel: 1547.8nm

Leading Channel: 1557.4nm

Trailing Channel: 1552.6nm

Signal In Signal Out Fiber

N×Δt N×Δt

Original

Signal Amplified

Signal

92

0

2

p

i

t eff

PN z u

N A z

(4.3)

Nt is the Erbium doping concentration. Replacing N2 in the propagation Equation 4.2 with

the Equation 4.3, the change of pump power along the fiber can be expressed as:

2 0 ( )p p

i i n p

t eff

P Pu u P z

z N A z

(4.4)

By solving this ordinary differential equation, we can obtain Pp(z, 0) and N2 (z, 0) by

replacing Pp(z, 0) back into Equation 4.3.

The transient gain is calculated by accumulating the gain of each small segment of the

signals going through each small piece of fiber. The whole process is shown in Figure 4.2.

At the last step, we will normalize both the original and amplified signal and compare the

amplitude difference of these two waveforms. The difference of the normalized

amplitude, if it exists (pulse-shape difference ≠ 0), is the distortion of the pulse-shape. As

the measurement of original electrical signal is based on the unfolding of the optical

signal, any distortion in the pulse-shape of the optical signal will result in deformed

reconstruction of the original electrical signal.

93

Figure 4.2 The schematic of the finite-difference method applied in the calculation of

transient gain in EDFAs.

Calculation boundary conditions of

N2(z, 0), Pp(z, 0)

2 0N

t

0

pP

t

Get N2 (z, 0) and Pp (z, 0)

Decompose Fiber and Signals into small

segments in length and time

Calculate the gain for each signal

segments going through the fiber

Reconstructure the signal

Normalize both original and amplified

signals and calculating the difference in

amplitude (Distortion)

94

4.2 Simulation parameters

The simulation requires the fiber parameters, including emission and absorption

coefficients for the pump and the signal wavelengths, the doping concentration, the fiber

core area and the spontaneous decay time.

1450 1470 1490 1510 1530 1550 1570 1590 1610 1630 1650-5

0

5

10

15

20

Wavelength (nm)

Absorp

tion a

nd E

mis

sio

n C

oeff

icie

nt

(dB

/m)

C-band: Absorption (Alpha) (dB/m)

C-band: Emission (g*) (dB/m)

L-band: Absorption (Alpha) (dB/m)

L-band: Emission (g*) (dB/m)

880 900 920 940 960 980 1000 1020 1040 1060 1080-2

0

2

4

6

8

10

12

Wavelength (nm)

Ab

so

rptio

n (

Alp

ha

) (d

B/m

)

L-band

C-band

(a) (b)

Figure 4.3 Absorption and Emission Coefficients of C- and L-band Erbium-doped fibers

at working wavelengths (a) and pump wavelengths (b). Data comes from [5].

From the data sheet, we can get emission and absorption coefficient (plotted in Figure 4.3)

and the fiber core area (Mode diameter = 5.26 μm). The spontaneous time is assumed to

be 10 ms [2-4]. However, the erbium doping concentration ranges from 9.0×1023

ions/m3

to 6.0×1026

ions/m3 from a variety of references. But neither the 3M data sheets for the

particular fibers that were used nor the commercial software (such as GainMaster)

provides this important parameter. So a moderate doping concentration 4×1024

ions/m3

was used in the simulation in this Chapter. The absorption at 1550nm provided by the 3M

95

data sheet is 3.32 dB/m [5]. The calculated absorption coefficient (α) (using Equation 4.5)

is 0.7645.

3.32 expout

in

P

P

(4.5)

The absorption cross-section (σ) at 1550nm varies slightly around 4.0×10-25

/m2 from

different references or manufacturers [6]. The overlapping factor (Г) at 1550nm was

assumed to be 0.5. Using Equation 4.6, the calculated Er3+

doping concentration (ρ) is

3.82 ×1024

ions/m3 which is very close the doping concentration (4.0 ×10

24 ions/m

3) used

in the simulation .

a (4.6)

For an 8m C-band Er-doped fiber with 100mW pump power, the boundary condition is

calculated and displayed in Figure 4.4(b). That result is compared with the result from the

commercial program “GainMaster” shown in Figure 4.4(a).

96

(a)

0 1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Position (m)

Inve

rsio

n L

eve

l

Calculated Result

Extracted Data from GainMaster

Interpolated from Extrated Data

(b)

(c)

Figure 4.4 The calculated boundary conditions. (a) GainMaster‟s result (b) the

comparison of the simulated result with the GainMaster‟s result (c) the EDFA

configuration for the boundary condition calculated with GainMaster shown in (a).

97

There are some differences between the simulated result and the result obtained with the

commercial software. The differences mostly come from the difference in fiber

parameters. GainMaster program has limited choices of Er-doped fibers. The emission

and absorption coefficients used in the simulation by GainMaster are closest to those of

the Er-doped fibers from 3M but not identical. Besides, the software only provides

wavelength dependent emission and absorption coefficients. But the fiber core area, the

doping concentration and the overlapping factors for the pump and signal wavelengths

are purposely kept unknown. Those parameters, especially the last three parameters, vary

over a wide range in different references. The effects of these parameters on the inversion

level along the fiber were calculated and shown in Fig 4.5.

Figure 4.5(a) is the change of inversion level (the fraction of the inverted photons) with

different overlap factors for the pump wavelength, the overlap factor for signal

wavelengths in calculation is 0.5. Figure 4.5(b) is the change of inversion level with

different signal (ASE) overlapping factors, the overlap factor for the pump in calculation

is 0.85. The inversion level decreases over the entire range of the fiber length with the

increase of the pump overlap factors. However, the initial inversion levels are almost the

same with different signal overlapping factors. Figure 4.5(c) is the change of inversion

level with different doping concentrations. Although the fiber core diameter is kept

unknown for the commercial software, the core diameters of most single mode fibers are

around 5μm. The small difference in diameter around 5μm (about ± 0.5μm) does not

result in as a large difference in inversion level as the other parameters do.

98

0 1 2 3 4 5 6 7 80.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Inve

rsio

n L

eve

l

p=0.1

p=0.3

p=0.5

p=0.7

p=0.9

0 1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Position (m)

Inve

rsio

n L

eve

l

s=0.1

s=0.3

s=0.5

s=0.7

s=0.9

(a) (b)

0 1 2 3 4 5 6 7 80.4

0.5

0.6

0.7

0.8

0.9

1

Position (m)

Inve

rsio

n L

eve

l

Nt= 2*10

24 /m

3

Nt= 6*10

24 /m

3

Nt= 1*10

25 /m

3

Nt= 1.4*10

25 /m

3

Nt= 1.8*10

25 /m

3

(c)

Figure 4.5 The relation between inversion level and different fiber parameters. (a)

Inversion level vs. overlap factor for the pump wavelength (b) Inversion level vs. overlap

factor for signal (ASE) wavelengths (c) Inversion level vs. doping concentration,

assuming overlap factors are 0.5 for both the pump and signal wavelengths.

99

0 1 2 3 4 5 6 7 8-0.02

0

0.02

0.04

0.06

0.08

0.1

Position (m)

Op

tica

l P

ow

er

(W)

EDFA Pump power vs. length

Pump (980nm)

Overall ASE Power (1450nm-1650nm)

Loss

(a)

0 1 2 3 4 5 6 7 8

0

1

2

x 10-4

Position (m)

Op

tica

l P

ow

er

(W)

1450nm

1470nm

1490nm

1510nm

1530nm

1550nm

1570nm

1590nm

1610nm

1630nm

1650nm

(b)

Figure 4.6 The change of optical powers along the fiber length. (a) Pump power, overall

ASE power (from 1450nm to 1650nm) and power loss vs. fiber length (b) ASE power at

different wavelengths vs. fiber length.

Another important reason for the difference between the calculated result and the

GainMaster‟s result is the ASE flux. The GainMaster calculated both forward and

100

backward ASE from 1520nm to 1620nm. To simplify the calculations, the backward ASE

in the simulation was ignored or treated as additional CW signal channels. In Figure

4.6(a), the accumulation of the overall ASE power along with the fiber was plotted. The

ASE wavelengths range from 1450nm to 1650nm with 0.2nm separation. The red line

represents the system power loss which equals to the initial pump power minus the

overall power (residual pump power + the overall ASE power) at each position. The

initial negative region of the red line (represents negative loss) comes from the round off

errors in the Matlab program. The overall power loss reaches the maximum at the fiber

length around 4m and then decreases with the accumulation of the ASE power along the

propagation direction. The power loss results from the difference in energy between the

pump and signal photons. Figure 4.6(b) is the optical power vs. fiber length at ten

different ASE wavelengths. From this plot, the optical powers of all wavelengths

accumulate during the forward propagation and the only exception is the 1530nm. For

this wavelength, the optical power reaches the maximum at the fiber length about 2.5m

and then decreases with the propagation. The calculation of the wavelength dependent

ASE powers can help the design for optical filters for the efficient ASE noise removal in

EDFAs.

The difference in the inversion levels along the fiber will result in the difference in the

fiber gain. The parameters used in the following simulations are: 0.85 and 0.5 for

overlapping factors with the pump and the signal wavelengths. The doping concentration

is 4×1024

ions/m3. With these parameters, the calculated gain closely matched the

experimentally measured value using these parameters.

101

4.3 Simulation results and discussion

Figure 4.7 is the typical signal pattern in the DANTEEO system. The holding channel is

shown in black and the two signal channels are shown in red and blue. The simulation,

assumed a zero background level and the maximum input amplitude of each three

channels is 1mV reading, which is very close to the real experimental conditions. The

photodetector used in the experiments and the DANTEEO system is DSC50S (Discovery

Semiconductors, Inc.), which has the responsivity 0.8 mA/mW. The characteristic

impedance for the oscilloscope is 50 Ohm. So the optical power according to 1 mV

reading from the oscilloscope equals 25 μW ( (1 mV/50 Ohm) / (0.8 mA/mW) = 0.025

mW ). The temporal resolution is 25 ps. The highest resolution for our digital

oscilloscope (TEKTRONIX TDS6604) is 50 ps. For 25 ps resolution, the oscilloscope

will automatically interpolate the data. The holding channel wavelength is 1547.72nm

and the wavelengths of two signal channels are 1552.52nm and 1557.36nm.

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5

Time (s)

Am

plit

ud

e (

a.u

.)

Holding Channel (1547.8nm)

Leading Channel (1557.4nm)

Trailing Channel (1552.8nm)

Figure 4.7 Waveforms of the signals in the DANTEEO system.

102

4.3.1 Single-stage forward pumping EDFAs

Figure 4.8 shows the experimental configuration used in the simulation. The length of the

C-band Erbium-doped fiber in simulation is 4.5m.

Figure 4.8 Schematic of the single-stage forward pumping EDFA configuration in

simulations.

C-band

WDM

Pumping

Signal

Signal

Residue Pumping

Drop-off

WDM Detector Oscilloscope

103

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Input Signal

Output Signal

40*(Input-Output)

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500

-0.005

0

0.005

0.01

0.015

0.02

0.025

Time (ns)

No

rma

lize

d A

mp

litu

de

Diffe

ren

ce

40*(Input-Output)

(a) (b)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Input Signal

Output Signal

40*(Input-Output)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (ns)

No

rma

lize

d A

mp

litu

de

Diffe

ren

ce

40*(Input-Output)

(c) (d)

Figure 4.9 Waveforms and gain plots with 60mW pump power. The signals from the first

and the second channels are shown in (a) and (c). The differences between the

renormalized signals are shown in (b) and (d), corresponding to (a) and (c).

The normalized waveforms and the gain plots with 60 mW pumping power are shown in

Figure 4.9 (a) and (c), including the waveforms of the first and second channels. The blue

curve shows the amplitude difference between the normalized input signal waveform and

the calculated amplified signal waveform. As the difference is very small compared with

signal amplitudes, this difference is multiplexed by 40 times. Figure 4.9(b) and (d) are the

104

detailed amplitude differences. In terms of these two plots, the amplitudes of the

distortion (=maximum-minimum, illustrated in the small plot in Fig 4.11) are close to

each other (about 0.02/40 = 0.05%) for two channels, but the temporal patterns are

different. The amplitude differences (distortion) of the first channel have the same signs

(except the first pulse) while they change the signs in the second channel. This means that

the amplitudes of the individual pulses (except the first pulse) from the first channel are

compressed to different extents at the EDFA output. However, the amplitudes of the

initial two pulses from the second channel are increased instead of deduction. The

distortions within the same channel are different from pulse to pulse. So the pulses within

the pulse train for each channel are not uniformly amplified, otherwise the amplitude

difference should always be zero or constant across the whole temporal profile. The

amplitude difference between the input and output for each channel also agrees with the

experiments. The second channel normally had higher distortion than the first channel,

and the second set of the pulses within the channel had higher distortion than the first set

of four pulses.

105

0 1000 2000 3000 4000 5000 6000-6

-5

-4

-3

-2

-1

0x 10

-6

Time (ns)

dG

/dt

((G

ain

)/n

s)

60 mW Pumping Power

Holding Channel

Leading Channel

Trailing Channel

3500 4000 4500 5000 5500

10-7

10-6

10-5

10-4

10-3

Time (ns)

log

(Ga

in)

60 mW Pumping Power

Leading Channel

Trailing Channel

(a) (b)

Figure 4.10 Simulated results (a) The derivative of the gain with respect to time vs. time

for three channels. (b) The semi-log plots of gain vs. time for two signal channels.

Figure 4.10(a) is the calculated differential gain vs. time. In the plots, all three channels

arrive at the Er-doped fiber at “0” ns. Before “0” ns, the Er-doped fiber is free of any

signals except the CW pump wavelength and the holding wavelength. Before 3500ns, the

amplitudes of signal channels (blue and red) are about 0.1 mV, 1/10 of the amplitude of

the holding channel (black). The derivative of the gain with respect to time, dG/dt,

undergoes a sudden fall-off at the start time because of the addition of three channels. To

avoid this transient change of the gain from the sudden addition of channels at the start of

the simulation, the input amplitudes for all channels are held at constant, nonzero powers

until the system reaches equilibrium. After the initial transient at the start of the

simulation, the system goes into equilibrium and the input signals are allowed to vary.

The dG/dt plateau from 3500ns to 5500ns comes from the CW power levels being turned

off in preparation for the arrival of the signal transients. The gain shown in Figure 4.10(b)

106

is the semi-log plot of the gains in two signal channels. As seen from Figure 4.9 (d), the

amplitude difference changes sign for two pulse-set. So we use absolute value for

amplitude difference in the semi-log plot.

50 100 150 200 250 3004

4.5

5

5.5

6

6.5

7x 10

-4

Pumping Power (mW)

Am

plit

ud

e D

iffe

ren

ce

(In

pu

t-O

utp

ut)

Leading Channel

Trailing Channel

(a)

50 100 150 200 250 300-14

-12

-10

-8

-6

-4

-2x 10

-4

Pumping Power (mW)

Am

plit

ud

e D

iffe

ren

ce

(In

pu

t-O

utp

ut)

Leading Channel

Trailing Channel

(b)

Figure 4.11 The amplitude differences under different pump powers. (a) The maximum

values of amplitude difference vs. pumping power (b) The minimum values of amplitude

difference vs. pumping power. The small plot shows the definition of max and min values

of the amplitude differences.

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (ns)

No

rma

lize

d A

mp

litu

de

40*(Input-Output)max

min

107

The simulations were done with the pump powers varying from 60mW to 300mW. The

relative distortion (for example Figure 4.9 (b) and (d)) are nearly independent of the

pump powers (the first and second channel respectively). However, the amplitudes of

peaks and valleys change with different pump powers. The amplitude differences vs.

pumping powers are shown in Figure 4.11. Unlike Figure 4.9 (b) and (d), the amplitude

differences in Figure 4.11 are the actual calculated results, not multipled by a factor of 40.

Figure 4.11 (a) is the maximum amplitude differences for two signal channels, which are

actually the amplitude differences of the maximum peaks. The amplitude differences in

peaks increase with the increasing of the pump powers, which means that the amplitude

compression of the amplified signals increases with the increasing of the pump power.

Figure 4.11 (b) is the minimum amplitude differences for two signals channels, which is

actually the amplitude differences of the valleys. The absolute values of amplitude

difference also increase with the increasing of pump powers, which means that the

amplitudes of the valleys in the first and second channels also increase with the

increasing of the pumping powers. If we define the level of distortion for a channel by the

difference between the maximum and the minimum amplitude difference, the second

channel always has higher pulse shape distortion than the first channel with all pump

powers.

Figure 4.12 are the gains and differential gains with different pump powers. All the

differential gain plots have an initial sharp decrease of dG/dt because of the instantaneous

addition of channels. For small pump powers (such as 120 mW), the first channel has

lower decreasing rate of the optical gain than the second channel. With the increasing of

108

the pump powers, the dG/dt rate for the first channel gets slower than that for the second

channel.

0 1000 2000 3000 4000 5000 6000-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0x 10

-5

Time (ns)

dG

/dt

((G

ain

)/n

s)

120 mW Pumping Power

Holding Channel

Leading Channel

Trailing Channel

0 1000 2000 3000 4000 5000 6000

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3x 10

-5

Time (ns)d

G/d

t(

(Ga

in)/

ns)

180mW Pumping Power

Holding Channel

Leading Channel

Trailing Channel

(a) (b)

0 1000 2000 3000 4000 5000 6000

-3

-2

-1x 10

-4

Time (ns)

dG

/dt

((G

ain

)/n

s)


Holding Channel

Leading Channel

Trailing Channel

0 1000 2000 3000 4000 5000 6000

-7

-6

-5

-4

-3

-2

-1x 10

-4

Time (ns)

dG

/dt

((G

ain

)/n

s)


Holding Channel

Leading Channel

Trailing Channel

(c) (d)

Figure 4.12 Gain and differential gain with different pump powers. (a) 120 mW (b) 180

mW (c) 240 mW (d) 300 mW.

109

4.3.2 Double-stage EDFAs

The transient response of the double-stage EDFA, used in the DANTEEO system for

higher gain (experimental results shown in Chapter 3) was also simulated.

Figure 4.13 Schematic of the double-stage, forward pumping configuration in simulations.

Figure 4.13 is the simple illustration of a double stage dual forward pumping scheme. In

the simulation, the pump power for both stages is 120mW. The lengths of the C-band Er-

doped fibers are 2m for the first stage and 4.5m for the second stage. The transit times for

the first and second fibers are 10 ns and 22.5 ns respectively. The temporal length of each

single pulse is 100ns (not FWHM but the full length). So when the leading edge of the

individual pulse leaving the second fiber, the trailing edge of that pulse has not yet

entered the amplifier chain if the transit time of the filter (or any other optical

components between the stages in the experiments) is less than 67.5 ns (=100ns - 10ns -

22.5ns). In this simulation, we assumed that the gain dynamics of the leading edge of the

signal in the second fiber will not affect the gain dynamics of the trailing edge of the

signal in the first fiber. A filter is added between the two stages to remove the residual

C-band

WDM

Pumping

Signal WDM

Detector Oscilloscope

C-band

Pumping

Signal

WDM

Residue Pumping

Drop off

Filter

110

980nm pump light. In the experiment, there was no filter for the 980nm light after the

first stage. There would be very small amount of residual pump power (much less than

0.1% if not over-pumping) of the first stage launching into the second stage. But for

simplification in simulation we assumed that the pumping of the first stage will not affect

the inversion level of the second stage.

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Input Signal

Output Signal

40*(Input-Output)

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Time (ns)

No

rma

lize

d A

mp

litu

de

Diffe

ren

ce

40*(Input-Output)

(a) (b)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

No

rma

lize

d A

mp

litu

de

Input Signal

Output Signal

40*(Input-Output)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time (ns)

Norm

aliz

ed

Am

plit

ud

e D

iffe

ren

ce

40*(Input-Output)

(c) (d)

Figure 4.14 Waveforms and gain plots with the double stage dual forward pumping

EDFA configuration shown in Figure 4.13. The signals from the first and the second

channels are shown in (a) and (c). The differences between the renormalized signals are

shown in (b) and (d), corresponding to (a) and (c).

111

0 1000 2000 3000 4000 5000 6000-8

-7

-6

-5

-4

-3

-2

-1x 10

-3

Time (ns)

dG

/dt

((G

ain

)/n

s)

Holding Channel

Leading Channel

Trailing Channel

3500 4000 4500 5000 5500

10-7

10-6

10-5

10-4

10-3

10-2

Time (ns)

log

(Ga

in)

Leading Channel

Trailing Channel

(a) (b)

Figure 4.15 Gain plots for the double stage dual forward pumping EDFA configuration

shown in Figure 4.13. (a) The differential gain for three channels. (b) The semi-log plots

of gain in signal channels.

Figure 4.14 are the signal waveforms of the double stage EDFA with the dual forward

pumping scheme as shown in Figure 4.13. Figure 4.15 shows the corresponding

differential gain and the semi-log plots of the time-dependent gain. This pumping scheme

looks like the single stage forward pumping scheme as the amplitude difference patterns

shown in (b) and (d) are very similar to the single-stage version (Figure 4.9 (b) and (d))

but with about 1.5 times higher amplitudes. The higher amplitude means that the double

stage forward pumped EDFA has higher pulse shape distortion than the single stage

forward pumped EDFA.

112

50 100 150 200 250 3000.8

1.2

1.6

2

2.4

2.8x 10

-3

Am

plit

ud

e D

iffe

ren

ce

(m

ax)

50 100 150 200 250 300-0.02

-0.015

-0.01

-0.005

0

Pumping Power (mW)

Am

plit

ud

e D

iffe

ren

ce

(m

in)

Leading Channel

Trailing Channel

Leading Channel

Trailing Channel

(a)

50 100 150 200 250 3007.2

7.6

8

8.4

8.8x 10

-4

Am

plit

ud

e D

iffe

ren

ce

(m

ax)

Pump Power (mW)

50 100 150 200 250 300-1.3

-1.2

-1.1

-1

-0.9

x 10-3

Am

plit

ud

e D

iffe

ren

ce

(m

in)

Leading Channel

Trailing Channel

Leading Channel

Trailing Channel

(b)

Figure 4.16 The change of amplitude differences with different pump powers for the

double-stage forward pumping configuration shown in Figure 4.13. (a) The change of

amplitude differences (max and min) with the change of pump powers for the second

stage, the pumping power for the first stage is 60mW. (b) The change of amplitude

differences (max and min) with the change of pumping powers for the first stage, the

pumping power for the second stage is 60mW.

Figure 4.16 displays plots of the change of amplitude differences (distortion) with the

change of pump powers of the dual forward pumped double-stage EDFA (the

50 100 150 200 250 3000.8

1.2

1.6

2

2.4

2.8x 10

-3

Am

plit

ud

e D

iffe

ren

ce

(m

ax)

50 100 150 200 250 300-0.02

-0.015

-0.01

-0.005

0

Pumping Power (mW)

Am

plit

ud

e D

iffe

ren

ce

(m

in)

Leading Channel

Trailing Channel

Leading Channel

Trailing Channel

113

configuration is shown in Figure 4.13). The solid lines (in blue and red) in Figure 4.16 (a)

and (b) represent the relations between the maximum amplitude differences and the pump

powers for the first and second stage respectively. From the plots, the increasing of the

pump powers for the first stage results in higher distortions than that for the second stage.

The dashed lines (in blue and red) in Figure 4.16 (a) and (b) represent the relations

between the minimum amplitude differences and the pump powers for the first and

second stage respectively. As with the maximum amplitude differences, the changes of

the pump powers for the first stage have a larger impact than those for the second stage.

Figure 4.17 Configuration of a double stage EDFA with forward and backward pumping

scheme.

Figure 4.17 is the configuration of the double stage EDFA with forward and backward

pumping scheme. As with the previous dual forward pumping in both stages simulation,

the assumption was made that the pumping of the first stage will not affect the inversion

level of the second stage, and vice versa. An isolator was added between the stages to

prevent backward flux. To compare with dual forward pumping scheme, the pumping

powers for the first and second stage are still 120mW and 120mW. The lengths of the C-

band Er-doped fiber are 2m and 4.5m.

C-band

WDM

Pumping

Signal WDM

Detector Oscilloscope

Isolator

C-band Pumping

Signal

114

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Input Signal

Output Signal

40*(Input-Output)

3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500-2

0

2

4

6

8

10

x 10-3

Time (ns)

No

rma

lize

d A

mp

litu

de

Diffe

ren

ce

40*(Input-Output)

(a) (b)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Input Signal

Output Signal

40*(Input-Output)

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500-4

-2

0

2

4

6

8

10

12

14x 10

-3

Time (ns)

Norm

aliz

ed

Am

plit

ud

e D

iffe

ren

ce

40*(Input-Output)

(c) (d)

Figure 4.18 Waveforms of the forward and backward pumped double-stage EDFA. The

configuration is shown in Figure 4.17. The signals from the first and the second channels

are shown in (a) and (c). The differences between the renormalized signals are shown in

(b) and (d), corresponding to (a) and (c).

Compared with the dual forward pumped EDFAs shown in Figure 4.13, the amplitude

differences of the forward and backward pumping scheme are obviously smaller in both

signal channels. The dG/dt plot of the dual forward pumping scheme is close to single-

stage EDFAs with an initial large decrease and then followed by a plateau with sharp

rising and falling edges. In the double stage forward and backward pumping scheme, the

115

derivative of gain with respect to time (dG/dt) has a rapid increase followed by a slow

decay in time. The sharp edges of the signal plateau from 3500ns to 5500ns turn into a

fast rise and a slow decay. These edges are magnified in Figure 4.19 (b).

0 1000 2000 3000 4000 5000 6000

0

0.2

0.4

0.6

0.8

1

Time (ns)

dG

/dt

((G

ain

)/n

s)

Holding Channel

Leading Channel

Trailing Channel

3500 4000 4500 5000 5500 6000

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

Time (ns)

dG

/dt

((G

ain

)/n

s)

Holding Channel

Leading Channel

Trailing Channel

(a) (b)

3500 4000 4500 5000 550010

-7

10-6

10-5

10-4

10-3

Time (ns)

log

(Ga

in)

Leading Channel

Trailing Channel

(c)

Figure 4.19 Gain plots with the forward and backward pumped double-stage EDFA. The

configuration is shown in Figure 4.17. (a) The differential gain for three channels. (b)

Zoom-in of the time region within red dashed line shown in (a). (c) The semi-log plots of

the gain for signal channels.

116

50 100 150 200 250 3000

1

2

3

4x 10

-4

Am

plit

ud

e D

iffe

ren

ce

(m

ax)

Pump Power (mW)

50 100 150 200 250 300-2

-1.5

-1

-0.5

0x 10

-4

Am

plit

ud

e D

iffe

ren

ce

(m

in)

Leading Channel

Trailing Channel

Leading Channel

Trailing Channel

(a)

50 100 150 200 250 3002.9

3

3.1

3.2

3.3x 10

-4

Am

plit

ud

e D

iffe

ren

ce

(m

ax)

Pump Power (mW)

50 100 150 200 250 300-5

-4

-3

-2

-1

0

1x 10

-7

Am

plit

ud

e D

iffe

ren

ce

(m

in)

Leading Channel

Trailing Channel

Leading Channel

(b)

Figure 4.20 The change of amplitude difference with pump power for the double stage

forward and backward pumping scheme. The configuration is shown in Figure 4.17. (a)

The change of amplitude difference (max and min) with the change of pumping power

for the second stage, the pump power for the first stage is 60mW. (b) The change of

amplitude difference (max and min) with the change of pump power for the first stage,

the pump power for the second stage is 60mW.

Figure 4.20 are the changes of the amplitude differences (distortion) with the change of

pump powers of two stages. Unlike the dual forward pumping scheme, the change of

117

pump power for the second stage does not change the amplitude difference of the second

signal channel (trailing channel). In Figure 4.20(b), the curve for the minimum amplitude

differences for the trailing channel was too small (10-7

~10-10

) to be plotted.

0 1000 2000 3000 4000 5000 6000675

680

685

690

695

700

705

710

715

720

Time (ns)

Ga

in

Holding Channel

Leading Channel

Trailing Channel

0 1000 2000 3000 4000 5000 6000

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

Time (ns)

Ga

in

Holding Channel

Leading Channel

Trailing Channel

(a) (b)

Figure 4.21 Gain vs. Time. (a) the double-stage with dual forward pumping (b) the

double-stage with forward and backward pumping.

Figure 4.21 compares the gain profiles of two double-stage pumping schemes. In terms of

the plots, the backward pumping in the second stage resulted in higher gain.

Based on the simulations of three different configurations of EDFAs (single-stage

forward pumping, double-stage dual forward pumping and double-stage forward and

backward pumping), we found that the double-stage with forward and backward pumping

schemes had the smallest distortion (amplitude difference) and the highest gain of all

pumping schemes. From the differential gain (dG/dt) plots (such as Figure 4.12, Fig

4.15(a) and Figure 4.19(b)), the difference in gains for time sequential pulses or the

pulses having fine time structure can be estimated. For example, the gains of the leading

118

and trailing edge of a pulse with 10ns length in time will have 1.5% difference if the

dG/dt is 1.5×10-3

/ns. For two pulses (same amplitude) with 1μs separation, the gain of the

second pulse is about 66.7% of the gain for the first pulse.

In practice, there are trade-offs between different pumping schemes. The model has many

assumptions (for example, ASE was not included in all of the simulations because that

greatly increases the simulation time and the noise of the photodetector was never

included). The double stage forward and backward pumping has shown low pulse shape

distortion in the simulations. However, it has higher ASE (both experimentally and

theoretically) than the double-stage EDFA with a dual forward pumping configuration.

We hope for low pulse-shape distortion, low ASE and high gain EDFA to increase SNR

from measurement. In the simulation, there was an isolator between the stages to avoid

the damage from the backward flux of the 2nd

stage pumping power. However, the

polarization sensitive isolator is not applicable in the DANTEEO system, as mentioned in

Chapter 2.

4.3.3 Applications of the simulation results in NIF DANTEEO system

The simulations of transient gains in the previous sections can be used to estimate the

pulse shape distortion of the analog signals in the NIF DANTEEO system.

119

0 1000 2000 3000 4000 5000 6000-8

-7

-6

-5

-4

-3

-2

-1x 10

-3

Time (ns)

dG

/dt

((G

ain

)/n

s)

Holding Channel

Leading Channel

Trailing Channel

(a)

50 60 70 80 90 100 110 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (ns)

Norm

aliz

ed A

mplit

ude

(b)

Figure 4.22 Estimation of the pulse shape distortion resulted from the gain difference

within a single pulse. (a) The calculated differential gain for a double-stage dual-forward

pumping EDFA, the same Figure as Figure 4.15(a). (b) A typical waveform of a single

pulse in the NIF DANTEEO system.

a b

120

The pulse shape distortion within each individual pulses and within a pulse train having a

long time window can be calculated. For example, the pulse shape distortion resulted

from the gain difference within a single pulse can be calcualted using the differential gain

plots. The Figure 4.22 (a) is the calculated differential gain for a double-stage dual

forward pumping EDFA with the pumping power. This Figure is the same as Figure

4.15(a). Figure 4.22 (b) is a typical waveform of a single pulse in NIF DANTEEO system.

From Figure 4.15(a), the differential gain for the trailing channel is about -1.4×10-3

/ns.

The red line between point “a” (in the leading edge of the pulse) and point “b” (in the

trailing edge of the pulse ) in Figure 4.15 (b) represents the FWHM (full width half

maxmium) of the pulse. The FWHM of this pulse is about 36 ns. The difference of the

gain between point “a” and point “b” can be calculated as the product of the length of the

time window and the differential gain, which equals -1.4×10-3

× 36 = -5.04 %. As a result,

the gain difference within the single pulse shown in Figure 4.15(b) is -5.04%.

The differential gain in Figure 4.22 (a) is calculated based on the assumption that the

overlapping factor at the signal wavelengths is 0.85. If the overlapping factor is 0.80 (a

6% change), the calculated differential gain for the trailing channel becomes -1.25×10-3

.

The difference of the gain for the pulse in Figure 4.22 (b) then equals -1.25×10-3

× 36 =

-4.5 %. A 6% change in overlapping factor at the signal wavelengths will result in about

0.5% decrease in the gain difference within a 36ns (FWHM) pulse.

Figure 4.23 (a) is the simple schematic of experimental setup for the long pulse train

generation and amplification via an EDFA (from RAM Photonics). The input signal

121

waveform is shown in Figure 4.23 (b). The time window is about 10 μs. The wavelength

of the pulses with higher amplitudes is 1549.3nm. The wavelength of the pulses with

lower amplitudes is 1550.9nm. A single stage forward pumping EDFA configuration was

used to simulate the gain of the whole pulse train. For simplicity, only one wavelength

(1549.3nm) was used in the simulation.

(a)

0 2000 4000 6000 8000 10000 12000 14000 16000-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

No

rma

lize

d A

mp

litu

de

Input Signal

(b)

Figure 4.23 Experimental setup for the simulation of the transient gain for a long time

window. (a) The schematic of the experimental setup. (b) The waveform of the input

signal train of the pulses with two wavelengths. The length of the signal train is about 10

μs.

Wavelength #1

Wavelength #2

AOM MZM

AOM MZM

RF DWDM

M

EDFA

Photo

Detector

Oscillo

-scope

Wavelength #1

1549.3nm

Wavelength #2

1550.9nm

122

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

No

rma

lize

d A

mp

litu

de

Single Stage EDFA 200mW Pumping

Commercial EDFA

Simulated Result

Figure 4.24 Comparison of the experimental and simulation results.

And therefore, all pulses within the pulse train have the same absorption and emission

cross sections in the simulation. The comparison of the experimental and calculated

results (both in depleted gain region) is shown in Figure 4.24. The red line represents the

calculated result and the black line represents the experimental results. The simulated

result agrees well with the experimental results.

The main point of this comparison between experimental and calculated results is to

validate the ability of the model to correctly predict the performance of an arbitrary

EDFA. This is not necessarily the best design of EDFA.

123

Reference

1. A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in

erbium-doped fiber amplifiers”, IEEE Photon Technol. Lett, vol. 2, pp. 714-717, Oct

1990.

2. Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average Inversion Level, Modeling and

Physics of Erbium-Doped Fiber Amplifiers”, IEEE Journal of Selected Topics in

Quantum Electronics, vol. 3, No. 4, Aug 1997.

3. P. R. Morkel and R. I. Laming, “Theoretical modeling of erbium-doped fiber

amplifiers with excited-state absorption”, Optics Letters, vol. 14, No. 19, 1989.

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amplifiers”, IEEE Photon Technol. Lett, vol. 6, No. 12, Dec 1990.

5. 3M datasheets for C- and L-band fibers with part number FS-ER-7A28 and FS-ER-

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2004.

124

Chapter 5: General principles on photon entanglements

Quantum entanglement is the property of a pair of particles, described by quantum

mechanical wave functions in which there is a correlation between the results of

measurements performed on entangled pairs, and this correlation is observed even though

the entangled pair may be separated by an arbitrarily large distance [1-5].

In this chapter, we will emphasize the principles of photon entanglement, especially the

energy-time entanglement. In the next chapter, we will discuss the effect of fiber

replicator on the state of entangled photons.

5.1 EPR paradox and Entanglement

In 1935 at Princeton University, Einstein and his two students, Podolsky and Rosen,

coauthored a paper with the title “Can Quantum Mechanical Description of Physical

Reality Be Considered Complete?” in which Einstein argued with the viewpoint that “a

sufficient condition for the reality of a physical quantity is the possibility of predicting it

with certainty, without disturbing the system” [6]. In this paper, Einstein argued with this

idea using a hypothetical system composed of a single particle having one degree of

freedom (either momentum or position). The detection of one variable will alter the

particle‟s state and thus make the other variable “no physical reality”. Then he went into

a more general condition for a combined system with two sub-systems having two

physical quantities that do not commute. Thus, the measurement of one quantity in one

125

system will affect the other quantity of another system. In a word, the two physical

quantities that do not commute will not have “simultaneous reality”. However, based on

quantum mechanics, the wave function can completely describe a system‟s state, which

means the actual measurement will not alter the system. Noting on this contradiction,

Einstein, Podolsky and Rosen argued that the quantum-mechanical description of

physical reality is not complete. This is the so called EPR paradox.

In 1950s, David Bohm suggested a solution for the EPR paradox using the idea of

“hidden variables” during his unsuccessful faculty career in Princeton University [7-8].

Bohm believed that “it is not necessary to give up a precise, rational, and objective

description of individual systems at a quantum level of accuracy”. He attributed the

failure of quantum mechanics to the loss of an unknown variable or a “hidden” variable.

With the supplement of this “hidden” variable, the physical process can be precisely

measured. Because of technical difficulties in the experiments at quantum levels at the

time, it was impossible to test the validity of both EPR and EPRB where “B” represents

Bohm‟s interpretation. The breakthrough happened in 1964 when John S. Bell came up

with his famous Bell inequalities to verify the hidden variable theory in real experiments.

The Bell inequalities are the physical quantities we can calculate from the experimental

results. If the system obeys the quantum mechanics, these inequalities will be violated.

However, if the hidden variable does exist, these inequalities will be satisfied. The

details will be described in the following section.

126

Schrödinger was the first person to use the term „entanglement‟ to describe this peculiar

connection between quantum systems [9-10]:

“When two systems, of which we know the states by their respective representatives,

enter into temporary physical interaction due to known forces between them, and when

after a time of mutual influence the systems separate again, then they can no longer be

described in the same way as before, viz. by endowing each of them with a representative

of its own. I would not call that one but rather the characteristic trait of quantum

mechanics, the one that enforces its entire departure from classical lines of thought. By

the interaction the two representatives [the quantum states] have become entangled.”

5.2 Bell-type inequalities

In 1964, John Bell utilized the EPRB set-up to construct a stunning argument, at least as

challenging as EPR, but he came to a different conclusion [11]. Bell considered an

experiment in which there is “a pair of spin one-half particles formed somehow in the

singlet spin state and moving freely in opposite directions”. Each is sent to two distant

locations at which measurements of spin are performed. Each measurement yields a

result of “+1” for a match or “-1” for a non-match. The results showed that with the

measurements oriented at intermediate angles between these basic cases, the existence of

local hidden variables would imply a linear variation in the correlation. However,

according to the quantum mechanical theory, the correlation varies as the cosine of the

angle. Bell's experiments rules out local hidden variables as a viable explanation of

127

quantum mechanics. He then constructed an inequality and proved that the quantum-

mechanical correlations could violate his inequality, but the correlations based on hidden

variable models must satisfy it. This is the well-known Bell inequality. The original that

Bell derived was [11]:

1 , , ,P b c P a b P a c

(5.1)

P is the correlation of paired particles at a, b and c status. P was replaced by E later to

avoid the implication that correlation is actually probability. However, his inequality is

not used in practice as it applies only to a very restricted set of hidden variable theories.

In 1969, John F. Clauser, Michael A. Horne, Abner Shimony and Richard A. Holt

derived an important form (CHSH form) of Bell‟s inequality so that it can be applied in

real experiments [12]. The usual form of the CHSH inequality is:

2

( , ) ( , ) ( , ) ( , )

S

S E a b E a b E a b E a b

(5.2)

The original derivation of CHSH form is quite complicated. Bell‟s 1971 derivation is

more general and easy to understand [13]. A brief derivation follows: ρ(λ) is the

probability of the source being in the state λ for any particular trial being given by the

density function, the integral of which over the complete space is 1. A and B are the

averages of the outcomes, and 1A & 1B . Then the correlation is given by:

, , ,E a b A a B b d (5.3)

128

If a, a', b, b' are alternative settings of the detectors, then:

, , , ,

, , , , , , , ,

, , , , , ,

E a b E a b E a b E a b

A a B b A a B b A a B b A a B b d

A a B b B b A a B b B b d

(5.4)

Whenever , , 0B b B b , , , 2B b B b , then Equation 5.4 can be

simplified as:

, , , ,

2 ,

E a b E a b E a b E a b

A a

(5.5)

As 1A and 1d by definition, then equation finally can be expressed as:

, , , , 2E a b E a b E a b E a b (5.6)

If the measured value |S| > 2, then Bell‟s inequality is violated. The violation of Bell‟s

inequalities implies that hidden-variable theories cannot account for some of the

correlations that may be present in nature. This means that physical states may be

inherently non-local for causally separated particles. The first convincing test of the

violations of Bell inequalities was performed by Aspect, Grangier and Roger [14-15].

They measured the linear polarization entanglement in photons emitted by a radiative,

atomic-cascaded, decay of calcium. Since then, using entangled photons created by

parametric down-conversion, violations of the CHSH forms of Bell's inequality have

been observed for various degrees of freedom including polarization, phase and

momentum, time and energy and etc [16-22].

129

5.3 Energy-time entanglement

The energy-time entanglement at telecomm wavelengths is considered to be very

promising for its potential applications in the future long-distance quantum

communications such as quantum key distribution (QKD) [23-24]. Compared with

polarization entanglements, the energy-time entanglement techniques can make use of

modern fiber communication systems without worrying about the polarization-mode

dispersion while propagating the light in long fibers.

Mandel and his colleagues (at the University of Rochester) first demonstrated the

interference effect between paired photons [25-26]. And this effect is now named as

Hong-Ou-Mandel (HOM) effect.

(a) (b)

Figure 5.1 Experimental setup of the HOM model (a) and the interference pattern (b) [26].

Figure 5.1(a) is the experimental setup Mandel and his colleagues used to measure the

coherence between photons. The 50/50 beam splitter (BS) and the two mirrors (M1 and

130

M2) generate four possible optical paths for the photons. The coincidence counts per unit

time were measured at different BS positions. The result is shown in Figure 5.1(b). The

coincidence rate drops to zero (called HOM dip) when the two photons experienced the

exactly same optical path, which implies a destructive interference. And the FWHM of

HOM dip was about the length of the photon wave packet.

For practical applications in communication system, high dimensional energy-time

entanglements are of great interest as this technique will increase the content of the

transmitted information (signal bandwidth). High dimensionality also implies the higher

information security (against eavesdroppers). Entangled states with D = 3 (qutrits), 4

(qudits), 12 and as high as D = 36 have been demonstrated in labs [27-31]. However,

quantum states with high dimensionality (D > 4) always include other freedoms such as

polarization, which is hard to be realized in practical long-distance fiber communication

system. Pure time-energy entanglements with high dimensions are not easily to be

generated. Ali-Khan and etc demonstrated a protocol for a large-alphabet QKD with over

10 bits [32]. However, this protocol suffered from high BER (bit error rate).

Fortunately, the fiber replicator is a natural/passive dimension maker, as the fiber

replicator can be regarded as an Nth

order interferometer (It is a cascade of the

interferometers shown in Figure 5.1(a) with fixed beam splitter positions). This thesis

will investigate the use of the fiber replicator to generate high-dimension, energy-time

entanglement.

131

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1. T. Honjo, S. W. Nam, H. Takesue1, Q. Zhang, H. Kamada1, Y. Nishida, O.Tadanaga,

M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z.Wang, K. Inoue1

and Y. Yamamoto, “Long-distance entanglement-based quantum key distribution over

optical fiber”, Optics Express, vol. 16, No. 23, Nov 2008.

2. S. Fasel, N. Gisin, G. Ribordy, and H. Zbinden, “Quantum key distribution over 30 km

of standard fiber using energy-time entangled photon pairs: a comparison of two

chromatic dispersion reduction methods”, Eur. Phys. J. D. 30, pp. 143-148 (2004).

3. M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal,

G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, A. Zeilinger,

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Anton Zeilinger, “High-fidelity transmission of polarization encoded qubits from an

entangled source over 100 km of fiber”, Optics Express, vol. 15, No. 12, June 2007.

5. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M.

Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek4, B. Ömer, M. Fürst,

M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter and A. Zeilinger,

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June 2007.

6. A. Einstein, B. Podolsky, N. Rosen, “Can Quantum Mechanical Description of

Physical Reality Be Considered Complete?”, Physics Review, vol. 47, May 1935.

7. D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden”

variables. I”, Phys. Rev, vol. 85, No. 2 , Jan 1952.

8. D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden”

variables. II”, Phys. Rev, vol. 85, N2. 2, Jan 1952.

9. E. Schr¨odinger, “Die gegenwrtige Situation in der Quantenmechanik,”

Naturwissenschaften, vol. 23, pp. 844, 1935.

10. J. D. Trimmer, “The Present Situation in Quantum Mechanics: A Translation of

Schrodinger‟s ‟Cat Paradox‟ Paper,” Journal of the American Philosophical Society, vol.

124, pp.323, 1980.

11. J. S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics, vol. 1, pp. 195, 1964.

12. J. Clauser, John, M. Horne, A. Shimony, R. Holt, “Proposed Experiment to Test

Local Hidden-Variable Theories”, Physical Review Letters, vol.23, pp. 880, 1969.

http://www.nature.com/nphys/journal/v3/n7/abs/nphys629.html#a4

132

13. J.S. Bell, “Speakable and Unspeakable in Quantum Mechanics (Collected Papers on

Quantum Philosophy)”, Cambridge, 1971.

14. A. Aspect, P. Grangier, G. Roger, “Experimental tests of realistic local theories via

Bell's theorem”, Phys. Rev. Lett, vol. 47, pp. 460, 1981.

15. A. Aspect, P. Grangier, G. Roger, “Experimental realization of Einstein-Podolsky-

Rosen-Bohm gedankenexperiment: A new violation of Bell's inequalities”, Phys. Rev.

Lett, vol. 49, pp.91 .1982.

16. A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, E. Kapon, “Polarization-

entangled photons produced with high-symmetry site-controlled quantum dots”, Nature

Photonics, March 7, 2010.

17. R. Rangarajan, M. Goggin, Paul. Kwiat, “Optimizing type-I polarization-entangled

photons”, Optics Express, vol.17, No 21, 2009.

18. P. Trojek H. Weinfurter, “Collinear source of polarization-entangled photon pairs at

nondegenerate wavelengths”, Applied Physics Letter, vol. 92, No 21, 2008.

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“Phase control of a longitudinal momentum entangled photon state by a deformable

membrane mirror”, Quantum Physices, Nov 19, 2009.

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energy entanglement”, Physics Review A, vol. 73, No 3, 2006.

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133

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134

Chapter 6: Experimental Setup and Discussion for two

photon entanglement

In this chapter, the two photon time-bin entanglements will be discussed. We will

emphasize the effect of the fiber replicator on photon entanglement states. The entangled

photons were produced through parametric down conversion.

6.1 Experimental Setup

6.1.1 Light source

A diode-pumped Nd:YLF master oscillator was used as the light source. This oscillator

can be operated at a single-frequency in CW mode or in a single-frequency Q-switch

mode [1]. The design of the laser is shown in Figure 6.1.

The pump laser is a single-stripe, 1.2-W, CW laser diode with the wavelength at 797nm.

The active element is a 4 mm diameter 5mm length, 1.1% Nd:YLF wedged and AR-

coated rod oriented with the Brewster prism to provide 1053 nm lasing. The acoustic-

optical modulator (AOM) is used as the Q-switch. The repetition rate of the laser is fixed

at 300 Hz. Piezoelectric translator (PZT) is used to change the cavity length. The whole

system is built in a metal box with a temperature control circuit.

135

(a)

(b)

Figure 6.1 Block diagram of the multipurpose Nd:YLF laser (a) the Q-switched pulse (b)

[1].

The actual output power of the pumping laser can be adjusted by changing the pumping

current of the diode laser through the laser diode driver. Normally, the pumping current

range we used is from 850-1020 mA depending on the Q-Switch RF level. The pulse

width can be adjusted by changing the RF level of the AOM as the RF level will affect

the optical transmission of the AOM. The peak power of the laser pulse is inversely

136

proportional to the pulse width (the pulse energy is constant). For the fiber replicator used

in the experiments, the separation between replicated pulses is 12.5 ns. There will be up-

conversion and down-conversion in the entanglement experiments, both of which have

low optical power conversion efficiency. So we need narrow laser pulse (a little bit

smaller than 12.5 ns) and high power (but less than the damage threshold which is about

1 GW/cm2 for 10 ns pulse at 1064 nm [2]). The high power is not used for the actual

entanglement experiments. Instead, the high power is needed to generate enough down

converted signals to align and couple the free-space optical power into single mode fibers

before the replicator. The narrowest pulse width for this laser is about 32-42 ns. So a

Mach-Zehnder modulator is used as soon as the light is injected into the optical fiber to

further carve the laser pulse to be less than 12.5 ns to avoid interference between different

temporal windows in the fiber replicator.

6.1.2 Time-bin entanglement system

The time-bin entanglement system is shown in Fig 6.2. IR Light from the Q-switch laser

described in the last section at 1053nm is used as the light source. The Pockels Cell

sandwiched between a pair of polarizers (shown within the red dashed line) was designed

to carve the laser pulse by modulating the polarization with the time. It could be bypassed

it with a half-wave plate to increase the alignment signal. The two BBOs in the setup

were the identical type I BBOs (2×2×5 mm) with AR coatings, although their non-linear

properties work in the opposite sense. The first BBO is used for up-conversion or second

137

harmonic generation (SHG) while the second BBO creates the paired photons via

spontaneous parametric down conversion (SPDC) [3].

Figure 6.2 Schematic of the time-bin photon entanglement system.

The SHG conversion efficiency is about several percent depending on the pulse peak

power. It is about 10-2

for the lower optical power conditions in this setup. The down-

conversion efficiency is normally 10-4

-10-5

or less. Combined together, the total

conversion efficiency should be 10-8

or less. To generate one pair of down-converted

photons at 1053nm per laser pulse, the input energy at 1053nm should be larger than

0.037 nJ (equals 1 mW peak power assuming the pulse width is 37 ns) or the input energy

138

at 527nm should be larger than 0.037 μJ. The transmission of the original IR light needs

to be lower than 10-8

after the first BBO to ensure that the detected signal is down-

converted IR photons instead of the original IR light directly from the laser. So we used

three KG5 filters to filter out the IR light. The internal transmission at about 1050nm for

KG5 glass is 3.5×10-5

. The total optical transmission coefficient is 4.2 ×10-14

for three of

them. There were two lens and three filter glasses between two BBO crystals. As the light

path was parallel to the optical axis the components, thus the polarization should not

change when light passing through these components. Therefore, there is no polarizer

between the BBO crystals for SHG (second harmonic generation) and SPDC

(spontaneous parametric down-conversion) processes. The entangled photons from SPDC

process are shown as a dashed line in Fig 6.2. After the SPDC process, three RG630

filters were used to remove the residual SHG light around 527nm. The transmission of

RG630 at 527nm±50nm is 10-5

. As the SHG is a nonlinear transition, the spectrum will

become wider. So with a “broadband” low transmission, all the residual SHG green light

is removed. As with eliminating the residual IR light, three cascaded glass filters were

used to ensure a high signal to noise ratio. The SPDC light was coupled into the fiber

using a five-axis fiber coupler. Two counter-propagating lasers were used for alignments.

A fiber laser at 635nm was used to align the light for high coupling efficiency. The SHG

green light was used for the fiber coupling alignment, as the SPDC was too weak to be

detected with conventional detectors. So the RG630 filters were temporarily removed to

align the system. The 635nm alignment light, which is shown as the orange line in Figure

6.2, goes the reverse optical path as the green light. By adjusting two mirrors, we can

139

align the optical path of the red light (635nm) so that its optical path coincides with the

green light. Two irises were used as both for alignment and exclusion of scattered and

environmental lights. To decrease noise photons from the scattering from the surfaces of

the optical components such as mirrors, lens and filters, there is a long light path before

coupling into the fiber.

A Mach-Zehnder modulator, before the 6-stage fiber replicator, was used to carve the

laser pulse width into ~11 ns pulse as measured by the oscilloscope. The entangled

photons have 26 different choices of optical path length. The two outputs of the fiber

replicator were connected to two avalanche photo detectors (APD) with fiber inputs. The

two APDs occupy two channels of the oscilloscope, while the third channel was the

reference light from the original 1053nm light. We will calculate the time difference

between the signals from each APD and the reference light. The 6-stage fiber replicator

has 64 temporal windows with 12.5 ns per window. As the detection resolution of the

digital oscilloscope is 100 ps, there are a total of 125 time slots (=12.5ns/100ps) per

window. If the detected two signals fall into the same time slot (even if they are in

different channels), the two signals might be entangled. If they are in different time slots,

the two signals are not entangled.

In order to increase the photon counting and recording efficiency of the digital

oscilloscope, we use the TTL “or” gate from both photodetectors as the trigger. Signals

from either or both photodetectors can trigger the oscilloscope. So only laser events that

happen to generate single photons hitting the APDs are recorded.

140

6.2 Characterization of photon distribution without SPDC

As the fiber replica is the key component to generate a Nth

order interference between

paired photons, we start our characterization/calibration process from this component.

600 700 800 900 1000 1100 1200 1300 14000

0.5

1

1.5

2

2.5

Time (ns)

Am

plit

ud

e (

a.u

.)

Output 1 (red fiber)

Output 2 (blue fiber)

(a)

0 10 20 30 40 50 60

11

12

13

14

15

16

17

18

19

20

Channel

Ch

an

ne

l W

idth

(n

s)

Output 1 (red fiber)

Output 2 (blue fiber)

(b)

Figure 6.3 Calibration of the fiber replicator (a) the oscilloscope waveform (b) the

calculated channel width.

141

Figure 6.3(a) is the pattern of pulses emerging from the 64-channel fiber replicator. Blue

and red curves represent the waveforms from the two different outputs. Based on these

plots, we can find the peak positions of each single pulse and then calculate the temporal

width of each channel. As the two outputs are theoretically symmetrical, the temporal

widths of each channel reading from two outputs should be identical. This is verified by

the results shown in Figure 6.3(b) that each channel is almost 12.5ns. The only exception

is the temporal distance between the 32th

and 33th

channel (19ns, about 50% above the

average). This wide width implies that the length of the fiber in the last stage is much

longer than it should be.

Figure 6.4 Schematic of the system for characterizing the outputs without SPDC.

The next step was to characterize the whole system as shown in Figure 6.4. To compare

with the SPDC condition, we did the measurements under no-entanglement condition by

142

removing two BBO crystals and all filters. Instead, glass attenuators were used to ensure

that the signal counts per hour was close to or even less than the condition of SPDC,

about 2-3 minutes per count. The oscilloscope starts recording the data after the TTL

signals (from either or both APDs) trigger. As the repetition rate of the laser pulse is 300

Hz (compared with the oscilloscope recording rate 2-3 min per count), a set of attenuators

were used to limit the photons hitting the APDs for each triggered event.

2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000-1

0

1

2

3

4

5

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Reference Laser

TTLs

APD #1

APD #2

Figure 6.5 Simultaneous signals from both channels of the fiber replicator. The photons

in this measurement are not entangled.

143

2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200-1

0

1

2

3

4

5

Time (ns)

No

rma

lize

d A

mp

litu

de

Reference Signal

TTLs

APD #1

APD #2

2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000-1

0

1

2

3

4

5

Time (ns)

No

rma

lize

d A

mp

litu

de

Reference Signal

TTLs

APD #1

APD #2

(a) (b)

2300 2400 2500 2600 2700 2800 2900 3000 3100 3200-1

0

1

2

3

4

5

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Reference Signal

TTLs

APD #1

APD #2

(c)

Figure 6.6 Multiple signals from the APDs. The photons in this measurement are not

entangled.

We recorded total 1000 counts (triggered events), over 41h18min, about 2-3 min per

count. The results are shown in Figure 6.5 and 6.6. There were always simultaneous

signals in each APD like Fig 6.5. There were also cases in which there are multiple

signals in APDs like Fig 6.6 (a) - (c). For total 1000 recorded counts, there were a total of

148 counts with multiple signals in one or both channels.

144

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

Channel

Rela

tive

Am

plit

ud

e

Figure 6.7 Amplitude Calibration of the 64× fiber replicator with 12.5 ns channel width.

The calibration of the fiber replicator is shown in Figure 6.7. This calibration was done

with the APDs. The fiber splitters between the stages are not perfectly balanced at a

50/50 ratio, so the probabilities of a photon hitting each temporal window are not strictly

equal. The statistical distribution of photons for the fiber replicator used in the SPDC

experiments matched the pulse height distribution when large number of photons entered

the replicator as shown in Figure 6.3 (a).

6.3 Characterization of time-bin entangled photon distribution

The typical signals from the oscilloscope are shown in Figure 6.8. Similar to the signals

without entangled photons, the entangled photons also have multi-pulse events within one

output port, as shown in (b) and (c), although a tri-pulse happened only once for a total of

1000 counting events. For photons without entanglement, every count recorded had one

145

pair of simultaneous pulses from both ports as shown in Figure 6.5 and 6.6. Although we

expected to get twin pulses from both channels for entangled conditions, we never get

two pulses from both output ports of the fiber replicator in more than 10000 recorded

events on different dates with two different oscilloscopes (Tektronix TEK4000 and

TDS6400). It is assumed that some optical components in the experimental setup may

forbid the appearance of twin pulses.

Table 6.1 Combinations of APDs and fiber replicator outputs (C1 and C2)

APD #1 APD #2

C1 ① ②

C2 ③ ④

In the entanglement experiments, the two detectors and the two outputs of the fiber

replicator should be equivalent to each other for meaningful results. In order to ensure the

equivalent detection efficiencies, the two photo detectors were the same model, with

nearly equal quantum efficiencies. The two photodetectors were tested under non-

entangled conditions by counting the photons with different photodetectors (APD #1 and

APD #2) and fiber replicator outputs (C1 and C2) combinations as shown in Table 6.1.

For the entanglement experiments, the focus was on the photon counts distribution over

the 64 time bins. In this experiment, it was only necessary to know the total counts over a

specific period of time from each output of the fiber replicator.

146

500 1000 1500 2000 2500-1

0

1

2

3

4

5

Time (ns)

No

rma

lize

d A

mp

litu

de

Reference Signal

TTLs

APD #1

APD #2

1000 1500 2000 2500 3000-1

0

1

2

3

4

5

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Reference Signal

TTLs

APD #1

APD #2

(a) (b)

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000-1

0

1

2

3

4

5

Time (ns)

Norm

aliz

ed

Am

plit

ud

e

Reference Signal

TTLs

APD #1

APD #2

(c)

Figure 6.8 Signals from the oscilloscope (a) single pulse (b) two pulses in one channel (c)

three pulses in one channel. The photons characterized in this figure are possibly

entangled through SPDC.

First, the total counts with the combination of ① and ④ within a period of time were

measured. Next the photodetectors (using the combination of ② and ③) were switched

and the total counts were measured again over the same time interval. The number of

147

events in condition ① is very close to the number in condition ③, and so does the

number in condition ②and ④. Thus, the two outputs of fiber replicator are equivalent.

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

9

Channel

Cou

nts

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

Channel

Co

un

ts

(a) (b)

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

9

10

Channel

Cou

nts

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

Channel

Cou

nts

(c) (d)

Figure 6.9 Counts per channel for the fiber replicator (a) and (c) are raw data from output

#1 and #2. (b) and (d) are calibrated data. These counts are for photons under entangled

state.

The counts per each channel for both outputs of the fiber replicator are shown in Figure

6.9. The statistical distribution of photons in the fiber replicator shown in Fig 6.7 is used

148

to calibrated/renormalized the original data shown in Fig 6.8 (a) and (c). The originals

counting events for each channel are renormalized by dividing the counts with the

probabilities of photon going through this channel. The renormalized results for two

channels are shown in Fig 6.9 (b) and (d).

We assumed that there would be one count from each channel for each recording under

the entangled situation. However, we only recorded double counts in only one of each

channel for each time as shown in Figure 6.8 (b) and (c). To figure out the relationship

between these double counts (to find out if they are entangled or not), we did some

mathematical process. The first step is to find the exact location for each pulse of double

pulses. As the channel width is not exactly the same for all 64 channels (shown as blue

blocks in Figure 6.10), we use the minimum value as the temporal channel width, 12ns.

The temporal resolution depends on the data acquisition resolution. We normally set the

resolution 0.1ns. So there are total 12/0.1=120 time bins for each channel. The time-bins

are separated with black thin line within the blue blocks shown in Figure 6.10.

149

2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time (ns)

Am

plit

ud

e (

a.u

.)

Reference Laser Pulse

Signal from APD

Figure 6.10 Experimental setup for the determination of pulse locations

Figure 6.10 is the typical signal (red) and reference pulse (black) waveforms. Point “a”

represents the peak of the reference pulse. Points “c” and “d” represent the position of

two TTL signals. Line “ab” represents the transit time for the optical path between the

reference pulse and the fiber replica. The distance (ac-ab) and (ad-ab) represent the signal

positions within the fiber replica. So the exact location of the pulse “c” can be calculated

as (shown as yellow line and arrow):

Index of channel =integer [(ac-ab) / 12ns]

Index of time bin within the channel = {(ac-ab) / 12ns - integer [(ac-ab) / 12ns]} × 120

a b c d

ab

ac

ad

Channel

Fiber

replicator

150

The same process is also applied to pulse “d”.

0 5 10 15 20 25 30 35 40

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Counts

Diffe

ren

ce

in

Po

sitio

ns

(% in

Ch

an

ne

l w

ith

12

ns le

ng

th)

(a)

0 8 16 24 32 40 48 56 64

0

8

16

24

32

40

48

56

64

Channels of the 1st pulse

Ch

an

ne

ls o

f th

e 2

nd

pu

lse

(b)

Figure 6.11 (a) The difference of time-bin locations for two pulses (b) the distribution of

channel for two pulses.

151

-12 -8 -4 0 4 8 120

1

2

3

4

5

Difference in Time (ns)

Eve

nts

Figure 6.12 The events vs. timing difference of twin pulses.

In the Figure 6.11(a), we plotted the difference of the time-bin for two pulses with ±0.025

error bars. For example, the first pulse is in the 5th

time-bin of one channel, the second is

in the 25th

time-bin of another channel. The difference in position (y-axis) was calculated

as (25-5)/120= 0.167. From the plots, the difference seems distributed in the whole area,

although most of them are in ±0.4. The red dashed line represents that the time-bin of the

two pulses are exactly in the same index of time bin.

Figure 6.11(b) plotted the channels for double pulses. X-axis is the channel for the first

pulse of twin pulses while y-axis represents the channel for the second pulse of twin

pulses. Except for some “noisy” spots, there seems a linear relationship between the

indexes of the channels for the double pulses.

Figure 6.12 plotted the counting events of the time difference of the time-bins for two

pulses (Δt of time-bins). Although the total counting events seemed not enough to

152

describe a detailed shape, it is obvious the events at around zero time different are the

maximum events.

The data described in this chapter were based on a total of 20,000 oscilloscope triggers

and up to 1500 triggers in each continuous data set including both entangled and non-

entangled conditions. Compared with the counts (at least a total of 10,000 each

continuous data set) and the rate of counts (at least several hundred per 10s) from other

published photon entanglement experiments (such as in reference [3]), the accumulated

data in our lab is insufficient to support a statistically complete description of the photon

entanglement with the fiber replicator. For a total of 42 triggered twin pulses (results

shown in Figure 6.11 and 6.12), the estimated error is about 6.48 based on the Poisson

distribution. However, these experiments still provide a method to explore the photon

entanglement with an all-fiber multistage interferometer.

153

Reference

1. A.V. Okishev, M.D. Skeldon, W. Seka, “A highly stable, diode-pumped master

oscillator for the OMEGA laser facility”, OSA TOPS vol. 26 Advanced Solid-State lasers,

1999.

2. The damage threshold for BBO crystal for SHG comes from the link:

http://www.dayoptics.com/products/material/NLO_crystal/BBO.htm.

3. I. A. Khan and J. C. Howell, “Experimental demonstration of high two-photon time-

energy entanglement”, Phys. Rev. A., vol. 73, 2006.

154

Chapter 7: Conclusions and Future Work

This thesis includes two major projects: the EDFA design for analog signal amplification

in the NIF DANTEEO system and the investigation of the time-bin photon entanglement

after the fiber replicator.

For the EDFA experiments, we tried different configurations to get higher SNR and

lower background than the commercial EDFA (from MANLIGHT). With the same and

higher amplification as the commercial ones, our EDFA works well in amplifying

without distortions. By comparison, the commercial EDFA can retain the original pulse

shape only for pulses with low temporal frequency structures. For pulses with higher

frequency temporal structures (above ≈0.2 GHz), the commercial EDFA cannot retain the

original pulse shape even in the middle amplification of its range (with pump laser

currents above 120mA). We also compared the spectrum and performance of EDFAs

with same configurations but using different Er-doped fibers. The EDFAs with C-band

Er-doped fibers have higher amplification and also higher noise while the EDFAs with L-

band Er-doped fibers have lower amplification and lower noise. High amplification will

increase the SNR. We achieved moderately high amplification and comparatively low

noise and background level with a two-stage EDFA using C-band Er-doped fibers in the

first stage and L-band Er-doped fibers in the second stage.

Besides, we also simulated the gain dynamics of our EDFAs. As our analog signals

change rapidly with respect to the fiber transit time, we used the finite element method to

simulate the transient gain. For this simulation model, we are interested in the pulse-

155

shape fidelity during amplification which is very important in the recovery of the original

electrical signal. We found that there is always pulse shape distortion although the

amplitude is fairly small (<0.1% change in the amplitude). The pulse shape distortion is

independent of the gain but related to the type of the Er-doped fibers, the configuration

(single stage or multiple stages) and the pumping schemes (forward pumping or

backward pumping). The simulation agrees well with the experimental results that the

two-stage with forward and backward pumping is the best choice for our DANTEEO

system considering the trade-off between high-pulse shape fidelity, high gain and lower

noise.

To improve and further our study on the EDFAs applied in the DANTEEO system, we

will expand the signal channels to the original designed seven-channels (the DWDM has

eight channels, one of them is used as a holding channel) and investigate the detailed gain

dynamics for multiple channels.

In the photon entanglement experiments, we explored the effect of fiber replicator on the

quantum status of the entangled photons. It was anticipated that signals would be detected

from both outputs of the fiber replicator with entangled photons. However, whenever

double counts were detected, it was always the case that the signal came from only one of

the two outputs. It was never the case that signals with entangled photons came from both

outputs. In contrast, when small numbers of single photons (not entangled) entered the

fiber replicator, the distribution of the counts was evenly distributed between the outputs.

We analyzed the data and found some relationship between these twin signals. However,

156

our experiments were still limited by the amount of counting events per unit time. To

improve the experiments, we will try to increase the counting rate. We have a total of 64

temporal bins from the fiber replicator. However, currently we only have about 1000

counting events for each experiment because of the instability of the laser, which means

about 15 counting events per channel. This counting number is still far below the number

necessary to obtain meaningful statistical results, as we have to consider dark counts from

the photodetectors. In order to obtain high SNR, we will need APD signals with high

repetition rate. With high repetition rate signals, we can further improve the system by

increasing the data acquisition rate from the digital oscilloscope.

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